def openConvexFromVertList(vertices, name=None, description=None, path=None): if vertices: gfFigure=[vertices]+[[]]*len(vertices[0]) gfFigure=gf.figureConvexHullUpdate(gfFigure) gf.figureOpen(gfFigure) else: gf.close() if figureInfo: figureInfo.setNameDescPath(name, description, path)
def openConvexFromVertList(vertices, name=None, description=None, path=None):
if vertices:
gfFigure = [vertices] + [[]] * len(vertices[0])
gfFigure = gf.figureConvexHullUpdate(gfFigure)
gf.figureOpen(gfFigure)
else:
gf.close()
if figureInfo:
figureInfo.setNameDescPath(name, description, path)
def commandCreateDual():
figures=objFigure.fromGfFigure(gf.figureGet())
for f in figures:
if not check.isFigureConvex(f):
raise RuntimeError("The figure is not convex")
if figureInfo:
name, desc = figureInfo.getNameDesc()
figures=[createDual(f) for f in figures]
gf.figureOpen(objFigure.toGfFigure(figures), True)
if figureInfo:
figureInfo.setNameDescPath("Dual of " + name, None)
def commandStellate(): figures=objFigure.fromGfFigure(gf.figureGet()) if figureInfo: name,desc=figureInfo.getNameDesc() figures=[stellateFigure(f) for f in figures] if name: name="Stellated " + name desc=None gf.figureOpen(objFigure.toGfFigure(figures), True) if figureInfo: figureInfo.setNameDescPath(name, desc)
def commandCreateDual():
figures=objFigure.fromGfFigure(gf.figureGet())
for f in figures:
if not check.isFigureConvex(f):
raise RuntimeError("The figure is not convex")
if figureInfo:
name, desc = figureInfo.getNameDesc()
figures=[createDual(f) for f in figures]
gf.figureOpen(objFigure.toGfFigure(figures), True)
if figureInfo:
figureInfo.setNameDescPath("Dual of " + name, None)
def commandCutOff(lastCoordinate=0):
gfFigure=gf.figureGet()
if gfFigure:
gfFigure[0]=[gf.posRotate(p) for p in gfFigure[0]]
figures=objFigure.fromGfFigure(gfFigure)
if not figures:
raise RuntimeError("Nothing opened")
dim=figures[0].spaceDim
hyperplane=algebra.Hyperplane((0,)*(dim-1)+(1,), lastCoordinate)
newFigures=[]
for f in figures:
newFigures.extend(cutFigure(f, hyperplane)[0])
gfFigure=objFigure.toGfFigure(newFigures)
if gfFigure:
gfFigure[0]=[gf.posRotateBack(p) for p in gfFigure[0]]
if figureInfo:
name, desc=figureInfo.getNameDesc()
gf.figureOpen(gfFigure, True)
if figureInfo:
figureInfo.setNameDescPath("Truncated "+name, None)
def commandCutFigure(lastCoordinate=0):
gfFigure=gf.figureGet()
gfFigure[0]=[gf.posRotate(p) for p in gfFigure[0]]
figures=objFigure.fromGfFigure(gfFigure)
if not figures:
raise RuntimeError("Nothing opened")
dim=figures[0].spaceDim
if dim<=0:
raise RuntimeError("The figure cannot be cut")
hyperplane=algebra.Hyperplane((0,)*(dim-1)+(1,), lastCoordinate)
newFigures=[]
for f in figures:
newFigures.extend(cutFigure(f, hyperplane)[1])
gfFigure=objFigure.toGfFigure(newFigures)
if gfFigure:
gfFigure[0]=[p[:-1] for p in gfFigure[0]]
del gfFigure[dim]
if figureInfo:
name, desc=figureInfo.getNameDesc()
gf.figureOpen(gfFigure)
if figureInfo:
figureInfo.setNameDescPath("Cross-section of "+name, None)
def commandCutFaces(dim=2, ratio=0.1):
if ratio>=1 or ratio<=0:
raise RuntimeError("Wrong ratio")
figures=objFigure.fromGfFigure(gf.figureGet())
for f in figures:
if not check.isFigureConvex(f):
raise RuntimeError("The figure is not convex")
if figureInfo:
name, desc = figureInfo.getNameDesc()
figures2=[]
for f in figures:
figures2.extend(cutOffFacesDim(f, ratio, dim))
gf.figureOpen(objFigure.toGfFigure(figures2), True)
gf.clear()
if dim==0:
name = name + " with vertices cut off"
elif dim==1:
name = name + " with edges cut off"
else:
name = name + " with " + str(dim) + "-faces cut off"
if figureInfo:
figureInfo.setNameDescPath(name, None)
import gf
gf.figureOpen([[(0.8164966106414795, 0.0, -0.5773502588272095),
(-0.8164966106414795, 0.0, -0.5773502588272095),
(0.0, 0.8164966106414795, 0.5773502588272095),
(0.0, -0.8164966106414795, 0.5773502588272095)],
[[0, 1], [0, 2], [1, 2], [0, 3], [1, 3], [2, 3]],
[[0, 2, 1], [0, 4, 3], [1, 5, 3], [2, 5, 4]], [[0, 1, 2, 3]]])
try:
import figureInfo
figureInfo.setNameDescPath(
'Regular Tetrahedron',
'3-simplex.\nOne of the five Platonic Solids (regular polyhedra).\nIts faces are triangular.',
__file__)
except ImportError:
pass
import gf
gf.figureOpen([[(-0.5, -0.5, -0.5, -0.5), (-0.5, -0.5, -0.5, 0.5), (-0.5, -0.5, 0.5, -0.5), (-0.5, -0.5, 0.5, 0.5), (-0.5, 0.5, -0.5, -0.5), (-0.5, 0.5, -0.5, 0.5), (-0.5, 0.5, 0.5, -0.5), (-0.5, 0.5, 0.5, 0.5), (0.5, -0.5, -0.5, -0.5), (0.5, -0.5, -0.5, 0.5), (0.5, -0.5, 0.5, -0.5), (0.5, -0.5, 0.5, 0.5), (0.5, 0.5, -0.5, -0.5), (0.5, 0.5, -0.5, 0.5), (0.5, 0.5, 0.5, -0.5), (0.5, 0.5, 0.5, 0.5), (-1.0, 0.0, 0.0, 0.0), (0.0, -1.0, 0.0, 0.0), (0.0, 0.0, -1.0, 0.0), (0.0, 0.0, 0.0, -1.0), (1.0, 0.0, 0.0, 0.0), (0.0, 1.0, 0.0, 0.0), (0.0, 0.0, 1.0, 0.0), (0.0, 0.0, 0.0, 1.0)], [[0, 1], [0, 17], [1, 17], [0, 18], [1, 18], [0, 8], [8, 18], [1, 9], [9, 18], [8, 9], [8, 17], [9, 17], [0, 2], [2, 17], [0, 19], [2, 19], [8, 19], [2, 10], [10, 19], [8, 10], [10, 17], [0, 4], [4, 18], [4, 19], [4, 12], [12, 19], [8, 12], [12, 18], [10, 14], [14, 19], [10, 20], [14, 20], [12, 14], [12, 20], [8, 20], [9, 13], [13, 18], [9, 20], [13, 20], [12, 13], [9, 11], [11, 17], [11, 20], [10, 11], [12, 21], [13, 21], [14, 21], [13, 15], [15, 21], [14, 15], [15, 20], [10, 22], [11, 22], [14, 22], [11, 15], [15, 22], [9, 23], [11, 23], [13, 23], [15, 23], [1, 23], [1, 3], [23, 3], [11, 3], [17, 3], [2, 22], [2, 3], [22, 3], [0, 16], [2, 16], [1, 16], [16, 3], [1, 5], [23, 5], [13, 5], [18, 5], [4, 21], [4, 5], [21, 5], [4, 16], [16, 5], [2, 6], [22, 6], [14, 6], [19, 6], [4, 6], [21, 6], [16, 6], [15, 7], [21, 7], [23, 7], [5, 7], [16, 7], [6, 7], [22, 7], [3, 7]], [[0, 2, 1], [0, 4, 3], [5, 6, 3], [7, 8, 4], [9, 8, 6], [5, 10, 1], [7, 11, 2], [9, 11, 10], [12, 13, 1], [12, 15, 14], [5, 16, 14], [17, 18, 15], [19, 18, 16], [17, 20, 13], [19, 20, 10], [21, 22, 3], [21, 23, 14], [24, 25, 23], [26, 25, 16], [24, 27, 22], [26, 27, 6], [28, 29, 18], [28, 31, 30], [32, 31, 33], [19, 30, 34], [26, 33, 34], [32, 29, 25], [35, 36, 8], [35, 38, 37], [39, 38, 33], [9, 37, 34], [39, 36, 27], [40, 41, 11], [40, 42, 37], [43, 42, 30], [43, 41, 20], [39, 45, 44], [32, 46, 44], [47, 48, 45], [49, 48, 46], [47, 50, 38], [49, 50, 31], [43, 52, 51], [28, 53, 51], [54, 55, 52], [49, 55, 53], [54, 50, 42], [40, 57, 56], [35, 58, 56], [54, 59, 57], [47, 59, 58], [60, 62, 61], [57, 62, 63], [2, 64, 61], [41, 64, 63], [7, 56, 60], [65, 67, 66], [52, 67, 63], [13, 64, 66], [17, 51, 65], [12, 69, 68], [70, 71, 61], [69, 71, 66], [0, 70, 68], [60, 73, 72], [58, 73, 74], [4, 75, 72], [36, 75, 74], [76, 78, 77], [45, 78, 74], [22, 75, 77], [24, 44, 76], [21, 79, 68], [70, 80, 72], [79, 80, 77], [65, 82, 81], [53, 82, 83], [15, 84, 81], [29, 84, 83], [76, 86, 85], [46, 86, 83], [23, 84, 85], [69, 87, 81], [79, 87, 85], [48, 89, 88], [59, 90, 88], [78, 91, 89], [73, 91, 90], [80, 91, 92], [87, 93, 92], [86, 93, 89], [55, 94, 88], [82, 93, 94], [71, 95, 92], [67, 95, 94], [62, 95, 90]], [[0, 1, 2, 3, 4, 5, 6, 7], [8, 9, 10, 11, 12, 5, 13, 14], [15, 16, 10, 17, 18, 2, 19, 20], [21, 22, 23, 24, 25, 26, 12, 18], [27, 28, 29, 30, 25, 31, 4, 20], [32, 33, 34, 30, 24, 35, 7, 14], [29, 36, 37, 38, 39, 23, 40, 41], [34, 42, 43, 44, 45, 22, 46, 41], [33, 47, 48, 49, 50, 28, 46, 40], [47, 51, 52, 53, 54, 6, 55, 32], [42, 56, 57, 58, 54, 13, 59, 35], [60, 53, 58, 61, 62, 63, 0, 8], [48, 64, 65, 66, 67, 3, 55, 27], [36, 68, 69, 70, 67, 19, 71, 31], [72, 66, 70, 73, 74, 63, 1, 15], [43, 75, 76, 77, 78, 11, 59, 21], [37, 79, 80, 81, 78, 17, 71, 26], [72, 77, 81, 82, 83, 60, 9, 16], [69, 84, 85, 86, 87, 65, 38, 50], [88, 86, 89, 90, 74, 83, 79, 68], [80, 84, 91, 90, 92, 76, 39, 45], [93, 94, 89, 92, 62, 82, 75, 56], [93, 95, 88, 87, 61, 73, 64, 51], [57, 91, 85, 94, 95, 52, 44, 49]], [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23]]])
try:
import figureInfo
figureInfo.setNameDescPath('Regular Icositetrachoron', 'Convex hull of the tesseract and regular hexadecachoron\nsharing their circumscribed spheres (and rotated appropriately).\nOne of the six regular polychora (4-dimensional analogy of Platonic solids).\nIts cells are octahedral.', __file__)
except ImportError: pass
import gf
gf.figureOpen([[(-1.0, ), (1.0, )], [[0, 1]]])
try:
import figureInfo
figureInfo.setNameDescPath('Abscissa', '1-simplex.\n1-cube.\n1-orthoplex.',
__file__)
except ImportError:
pass
import gf
import math
gf.figureOpen([[(math.sqrt(2) / 2, -math.sqrt(2) / 2),
(math.sqrt(2) / 2, math.sqrt(2) / 2),
(-math.sqrt(2) / 2, math.sqrt(2) / 2),
(-math.sqrt(2) / 2, -math.sqrt(2) / 2)],
[[3, 0], [0, 1], [1, 2], [2, 3]], [[0, 1, 2, 3]]])
try:
import figureInfo
figureInfo.setNameDescPath('Square', '2-cube.\n2-orthoplex.', __file__)
except ImportError:
pass
import gf
gf.figureOpen([[()]])
try:
import figureInfo
figureInfo.setNameDescPath('Point', '0-simplex.\n0-cube.', __file__)
except ImportError:
pass
import gf
gf.figureOpen([[(-1.0,), (1.0,)], [[0, 1]]])
try:
import figureInfo
figureInfo.setNameDescPath('Abscissa', '1-simplex.\n1-cube.\n1-orthoplex.', __file__)
except ImportError: pass
import gf
gf.figureOpen([[(0.8164966106414795, 0.0, -0.5773502588272095), (-0.8164966106414795, 0.0, -0.5773502588272095), (0.0, 0.8164966106414795, 0.5773502588272095), (0.0, -0.8164966106414795, 0.5773502588272095)], [[0, 1], [0, 2], [1, 2], [0, 3], [1, 3], [2, 3]], [[0, 2, 1], [0, 4, 3], [1, 5, 3], [2, 5, 4]], [[0, 1, 2, 3]]])
try:
import figureInfo
figureInfo.setNameDescPath('Regular Tetrahedron', '3-simplex.\nOne of the five Platonic Solids (regular polyhedra).\nIts faces are triangular.', __file__)
except ImportError: pass
import gf
gf.figureOpen([
[
(0.5, -0.8660253882408142),
(1.0, 0),
(0.5, 0.8660253882408142),
(-0.5, 0.8660253882408142),
(-1.0, 0),
(-0.5, -0.8660253882408142)
], [[4, 5], [5, 0], [0, 1], [1, 2], [2, 3], [3, 4]], [[0, 1, 2, 3, 4, 5]]])
try:
import figureInfo
figureInfo.setNameDescPath('Regular Hexagon', None, __file__)
except ImportError: pass
import gf
gf.figureOpen([[()]])
try:
import figureInfo
figureInfo.setNameDescPath('Point', '0-simplex.\n0-cube.', __file__)
except ImportError: pass
import gf
gf.figureOpen([[(-0.5, -0.5, -0.5, -0.5), (-0.5, -0.5, -0.5, 0.5), (-0.5, -0.5, 0.5, -0.5), (-0.5, -0.5, 0.5, 0.5), (-0.5, 0.5, -0.5, -0.5), (-0.5, 0.5, -0.5, 0.5), (-0.5, 0.5, 0.5, -0.5), (-0.5, 0.5, 0.5, 0.5), (0.5, -0.5, -0.5, -0.5), (0.5, -0.5, -0.5, 0.5), (0.5, -0.5, 0.5, -0.5), (0.5, -0.5, 0.5, 0.5), (0.5, 0.5, -0.5, -0.5), (0.5, 0.5, -0.5, 0.5), (0.5, 0.5, 0.5, -0.5), (0.5, 0.5, 0.5, 0.5)], [[12, 13], [12, 14], [13, 15], [14, 15], [9, 11], [9, 13], [11, 15], [10, 11], [10, 14], [8, 10], [8, 12], [8, 9], [1, 9], [1, 3], [11, 3], [0, 1], [0, 8], [2, 10], [2, 3], [0, 2], [1, 5], [13, 5], [4, 5], [4, 12], [0, 4], [2, 6], [14, 6], [4, 6], [15, 7], [3, 7], [5, 7], [6, 7]], [[0, 2, 3, 1], [4, 6, 2, 5], [7, 6, 3, 8], [8, 9, 10, 1], [5, 11, 10, 0], [4, 11, 9, 7], [12, 13, 14, 4], [15, 12, 11, 16], [17, 18, 14, 7], [15, 13, 18, 19], [19, 17, 9, 16], [12, 20, 21, 5], [22, 23, 0, 21], [15, 20, 22, 24], [24, 23, 10, 16], [17, 25, 26, 8], [23, 27, 26, 1], [19, 25, 27, 24], [28, 6, 14, 29], [2, 28, 30, 21], [13, 29, 30, 20], [3, 28, 31, 26], [18, 29, 31, 25], [22, 30, 31, 27]], [[0, 1, 2, 3, 4, 5], [6, 7, 8, 5, 9, 10], [11, 12, 7, 4, 13, 14], [15, 10, 16, 3, 17, 14], [1, 18, 19, 20, 6, 11], [2, 18, 21, 22, 8, 15], [21, 19, 23, 12, 0, 16], [9, 20, 22, 23, 13, 17]], [[0, 1, 2, 3, 4, 5, 6, 7]]])
try:
import figureInfo
figureInfo.setNameDescPath('Tesseract', '4-dimensional cube (4-cube).\nOne of the six regular polychora (4-dimensional analogy of Platonic solids).\nIts cells are cubical.', __file__)
except ImportError: pass
import gf
gf.figureOpen([[(-1.0, 0.0, 0.0, 0.0, 0.0), (0.0, -1.0, 0.0, 0.0, 0.0), (0.0, 0.0, -1.0, 0.0, 0.0), (0.0, 0.0, 0.0, -1.0, 0.0), (0.0, 0.0, 0.0, 0.0, -1.0), (1.0, 0.0, 0.0, 0.0, 0.0), (0.0, 1.0, 0.0, 0.0, 0.0), (0.0, 0.0, 1.0, 0.0, 0.0), (0.0, 0.0, 0.0, 1.0, 0.0), (0.0, 0.0, 0.0, 0.0, 1.0)], [[0, 1], [0, 2], [1, 2], [0, 3], [1, 3], [2, 3], [0, 4], [1, 4], [2, 4], [3, 4], [1, 5], [2, 5], [3, 5], [4, 5], [0, 6], [2, 6], [3, 6], [4, 6], [5, 6], [0, 7], [1, 7], [3, 7], [4, 7], [5, 7], [6, 7], [0, 8], [1, 8], [2, 8], [4, 8], [5, 8], [6, 8], [7, 8], [0, 9], [1, 9], [2, 9], [3, 9], [5, 9], [6, 9], [7, 9], [8, 9]], [[0, 2, 1], [0, 4, 3], [1, 5, 3], [2, 5, 4], [0, 7, 6], [1, 8, 6], [2, 8, 7], [3, 9, 6], [4, 9, 7], [5, 9, 8], [2, 11, 10], [4, 12, 10], [5, 12, 11], [7, 13, 10], [8, 13, 11], [9, 13, 12], [1, 15, 14], [3, 16, 14], [5, 16, 15], [6, 17, 14], [8, 17, 15], [9, 17, 16], [11, 18, 15], [12, 18, 16], [13, 18, 17], [0, 20, 19], [3, 21, 19], [4, 21, 20], [6, 22, 19], [7, 22, 20], [9, 22, 21], [10, 23, 20], [12, 23, 21], [13, 23, 22], [14, 24, 19], [16, 24, 21], [17, 24, 22], [18, 24, 23], [0, 26, 25], [1, 27, 25], [2, 27, 26], [6, 28, 25], [7, 28, 26], [8, 28, 27], [10, 29, 26], [11, 29, 27], [13, 29, 28], [14, 30, 25], [15, 30, 27], [17, 30, 28], [18, 30, 29], [19, 31, 25], [20, 31, 26], [22, 31, 28], [23, 31, 29], [24, 31, 30], [0, 33, 32], [1, 34, 32], [2, 34, 33], [3, 35, 32], [4, 35, 33], [5, 35, 34], [10, 36, 33], [11, 36, 34], [12, 36, 35], [14, 37, 32], [15, 37, 34], [16, 37, 35], [18, 37, 36], [19, 38, 32], [20, 38, 33], [21, 38, 35], [23, 38, 36], [24, 38, 37], [25, 39, 32], [26, 39, 33], [27, 39, 34], [29, 39, 36], [30, 39, 37], [31, 39, 38]], [[0, 1, 2, 3], [0, 4, 5, 6], [1, 4, 7, 8], [2, 5, 7, 9], [3, 6, 8, 9], [3, 10, 11, 12], [6, 10, 13, 14], [8, 11, 13, 15], [9, 12, 14, 15], [2, 16, 17, 18], [5, 16, 19, 20], [7, 17, 19, 21], [9, 18, 20, 21], [12, 18, 22, 23], [14, 20, 22, 24], [15, 21, 23, 24], [1, 25, 26, 27], [4, 25, 28, 29], [7, 26, 28, 30], [8, 27, 29, 30], [11, 27, 31, 32], [13, 29, 31, 33], [15, 30, 32, 33], [17, 26, 34, 35], [19, 28, 34, 36], [21, 30, 35, 36], [23, 32, 35, 37], [24, 33, 36, 37], [0, 38, 39, 40], [4, 38, 41, 42], [5, 39, 41, 43], [6, 40, 42, 43], [10, 40, 44, 45], [13, 42, 44, 46], [14, 43, 45, 46], [16, 39, 47, 48], [19, 41, 47, 49], [20, 43, 48, 49], [22, 45, 48, 50], [24, 46, 49, 50], [25, 38, 51, 52], [28, 41, 51, 53], [29, 42, 52, 53], [31, 44, 52, 54], [33, 46, 53, 54], [34, 47, 51, 55], [36, 49, 53, 55], [37, 50, 54, 55], [0, 56, 57, 58], [1, 56, 59, 60], [2, 57, 59, 61], [3, 58, 60, 61], [10, 58, 62, 63], [11, 60, 62, 64], [12, 61, 63, 64], [16, 57, 65, 66], [17, 59, 65, 67], [18, 61, 66, 67], [22, 63, 66, 68], [23, 64, 67, 68], [25, 56, 69, 70], [26, 59, 69, 71], [27, 60, 70, 71], [31, 62, 70, 72], [32, 64, 71, 72], [34, 65, 69, 73], [35, 67, 71, 73], [37, 68, 72, 73], [38, 56, 74, 75], [39, 57, 74, 76], [40, 58, 75, 76], [44, 62, 75, 77], [45, 63, 76, 77], [47, 65, 74, 78], [48, 66, 76, 78], [50, 68, 77, 78], [51, 69, 74, 79], [52, 70, 75, 79], [54, 72, 77, 79], [55, 73, 78, 79]], [[0, 1, 2, 3, 4], [4, 5, 6, 7, 8], [3, 9, 10, 11, 12], [8, 12, 13, 14, 15], [2, 16, 17, 18, 19], [7, 19, 20, 21, 22], [11, 18, 23, 24, 25], [15, 22, 25, 26, 27], [1, 28, 29, 30, 31], [6, 31, 32, 33, 34], [10, 30, 35, 36, 37], [14, 34, 37, 38, 39], [17, 29, 40, 41, 42], [21, 33, 42, 43, 44], [24, 36, 41, 45, 46], [27, 39, 44, 46, 47], [0, 48, 49, 50, 51], [5, 51, 52, 53, 54], [9, 50, 55, 56, 57], [13, 54, 57, 58, 59], [16, 49, 60, 61, 62], [20, 53, 62, 63, 64], [23, 56, 61, 65, 66], [26, 59, 64, 66, 67], [28, 48, 68, 69, 70], [32, 52, 70, 71, 72], [35, 55, 69, 73, 74], [38, 58, 72, 74, 75], [40, 60, 68, 76, 77], [43, 63, 71, 77, 78], [45, 65, 73, 76, 79], [47, 67, 75, 78, 79]], [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31]]])
try:
import figureInfo
figureInfo.setNameDescPath('Triacontaditeron', '5-dimensional octahedron (5-orthoplex).\nOne of the three regular 5-polytopes (5-dimensional analogy of Platonic solids).\nIts facets are pentachoral.', __file__)
except ImportError: pass
import gf
gf.figureOpen([[(-0.5, -0.5, -0.5, -0.5), (-0.5, -0.5, -0.5, 0.5), (-0.5, -0.5, 0.5, -0.5), (-0.5, -0.5, 0.5, 0.5), (-0.5, 0.5, -0.5, -0.5), (-0.5, 0.5, -0.5, 0.5), (-0.5, 0.5, 0.5, -0.5), (-0.5, 0.5, 0.5, 0.5), (0.5, -0.5, -0.5, -0.5), (0.5, -0.5, -0.5, 0.5), (0.5, -0.5, 0.5, -0.5), (0.5, -0.5, 0.5, 0.5), (0.5, 0.5, -0.5, -0.5), (0.5, 0.5, -0.5, 0.5), (0.5, 0.5, 0.5, -0.5), (0.5, 0.5, 0.5, 0.5), (-1.0, 0.0, 0.0, 0.0), (0.0, -1.0, 0.0, 0.0), (0.0, 0.0, -1.0, 0.0), (0.0, 0.0, 0.0, -1.0), (1.0, 0.0, 0.0, 0.0), (0.0, 1.0, 0.0, 0.0), (0.0, 0.0, 1.0, 0.0), (0.0, 0.0, 0.0, 1.0), (-0.80901700258255, -0.5, -0.30901700258255005, 0.0), (-0.80901700258255, -0.30901700258255005, 0.0, -0.5), (-0.80901700258255, 0.0, -0.5, -0.30901700258255005), (-0.5, -0.30901700258255005, -0.80901700258255, 0.0), (-0.30901700258255005, -0.80901700258255, -0.5, 0.0), (-0.30901700258255005, -0.5, 0.0, -0.80901700258255), (0.0, -0.5, -0.80901700258255, -0.30901700258255005), (-0.5, 0.0, -0.30901700258255005, 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1114], [463, 1129, 1130, 1131], [465, 1132, 1130, 1116], [699, 1133, 1134, 1120], [692, 1122, 1134, 1128], [673, 1135, 1136, 1127], [669, 1131, 1136, 1119], [353, 1110, 1132, 1133], [491, 1137, 1121, 1123], [176, 1108, 1138, 1129], [314, 1138, 1137, 1135], [536, 1139, 1140, 1141], [953, 1142, 1143, 1144], [925, 1145, 1146, 1144], [783, 1141, 1147, 1148], [785, 1149, 1148, 1143], [787, 1150, 1147, 1146], [231, 1151, 1152, 1153], [763, 1154, 1155, 1156], [1157, 1158, 1155, 1142], [769, 1159, 1156, 1145], [522, 1152, 1160, 1161], [196, 1151, 1162, 1163], [665, 1164, 1165, 1150], [661, 1161, 1165, 1159], [603, 1166, 1167, 1158], [602, 1168, 1167, 1149], [534, 1163, 1140, 1168], [413, 1153, 1139, 1164], [520, 1169, 1160, 1154], [309, 1162, 1169, 1166], [954, 1170, 1171, 1172], [1065, 1173, 1174, 1175], [1076, 1176, 1174, 1177], [1071, 1178, 1175, 1179], [1062, 1180, 1177, 1181], [1067, 1182, 1181, 1179], [1157, 1183, 1184, 1170], [993, 1185, 1186, 1187], [989, 1188, 1186, 1178], [984, 1172, 1187, 1182], [952, 1189, 1171, 1180], [605, 1190, 1183, 1191], [323, 1192, 1190, 1193], [648, 1193, 1194, 1195], [841, 1191, 1196, 1189], [1093, 1195, 1196, 1176], [764, 1197, 1184, 1185], [776, 1194, 1198, 1173], [1126, 1199, 1198, 1188], [674, 1192, 1197, 1199]], [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599]]])
try:
import figureInfo
figureInfo.setNameDescPath('Regular Hexacosichoron', 'One of the six regular polychora (4-dimensional analogy of Platonic solids).\nIts cells are tetrahedral.', __file__)
except ImportError: pass
import gf
import math
gf.figureOpen([[(math.sqrt(3) / 2, -0.5), (0, 1.0), (-math.sqrt(3) / 2, -0.5)],
[[2, 0], [0, 1], [1, 2]], [[0, 1, 2]]])
try:
import figureInfo
figureInfo.setNameDescPath('Regular Triangle', '2-simplex.', __file__)
except ImportError:
pass
import gf
import math
gf.figureOpen(
[
[
(math.sqrt(2) / 2, -math.sqrt(2) / 2),
(math.sqrt(2) / 2, math.sqrt(2) / 2),
(-math.sqrt(2) / 2, math.sqrt(2) / 2),
(-math.sqrt(2) / 2, -math.sqrt(2) / 2),
],
[[3, 0], [0, 1], [1, 2], [2, 3]],
[[0, 1, 2, 3]],
]
)
try:
import figureInfo
figureInfo.setNameDescPath("Square", "2-cube.\n2-orthoplex.", __file__)
except ImportError:
pass
[34, 42, 43, 44, 45, 22, 46, 41],
[33, 47, 48, 49, 50, 28, 46, 40],
[47, 51, 52, 53, 54, 6, 55, 32],
[42, 56, 57, 58, 54, 13, 59,
35], [60, 53, 58, 61, 62, 63, 0, 8],
[48, 64, 65, 66, 67, 3, 55, 27],
[36, 68, 69, 70, 67, 19, 71, 31],
[72, 66, 70, 73, 74, 63, 1, 15],
[43, 75, 76, 77, 78, 11, 59, 21],
[37, 79, 80, 81, 78, 17, 71, 26],
[72, 77, 81, 82, 83, 60, 9, 16],
[69, 84, 85, 86, 87, 65, 38, 50],
[88, 86, 89, 90, 74, 83, 79, 68],
[80, 84, 91, 90, 92, 76, 39, 45],
[93, 94, 89, 92, 62, 82, 75, 56],
[93, 95, 88, 87, 61, 73, 64, 51],
[57, 91, 85, 94, 95, 52, 44, 49]],
[[
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,
17, 18, 19, 20, 21, 22, 23
]]])
try:
import figureInfo
figureInfo.setNameDescPath(
'Regular Icositetrachoron',
'Convex hull of the tesseract and regular hexadecachoron\nsharing their circumscribed spheres (and rotated appropriately).\nOne of the six regular polychora (4-dimensional analogy of Platonic solids).\nIts cells are octahedral.',
__file__)
except ImportError:
pass
(0.35682210326194763, 0.9341723322868347, 0.0),
(0.9341723322868347, 0.0, 0.35682210326194763),
(0.0, 0.35682210326194763, -0.9341723322868347),
(0.35682210326194763, -0.9341723322868347, 0.0),
(-0.9341723322868347, 0.0, 0.35682210326194763),
(0.0, -0.35682210326194763, 0.9341723322868347),
(-0.35682210326194763, 0.9341723322868347, 0.0),
(0.9341723322868347, 0.0, -0.35682210326194763),
(0.0, -0.35682210326194763, -0.9341723322868347),
(-0.35682210326194763, -0.9341723322868347, 0.0),
(-0.9341723322868347, 0.0, -0.35682210326194763)],
[[5, 10], [5, 14], [8, 14], [7, 10], [7, 8], [2, 11], [2, 15],
[9, 15], [6, 11], [6, 9], [4, 12], [4, 16], [10, 16], [5, 12],
[6, 16], [7, 9], [4, 17], [11, 17], [0, 17], [0, 18], [12, 18],
[1, 14], [1, 18], [0, 19], [2, 19], [13, 19], [1, 13], [8, 3],
[13, 3], [15, 3]],
[[0, 3, 4, 2, 1], [5, 8, 9, 7, 6], [10, 13, 0, 12, 11],
[3, 15, 9, 14, 12], [11, 14, 8, 17, 16], [18, 16, 10, 20, 19],
[21, 1, 13, 20, 22], [23, 18, 17, 5, 24], [19, 22, 26, 25, 23],
[27, 2, 21, 26, 28], [7, 15, 4, 27, 29], [28, 25, 24, 6, 29]],
[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]]])
try:
import figureInfo
figureInfo.setNameDescPath(
'Regular Dodecahedron',
'One of the five Platonic Solids (regular polyhedra).\nIts faces are pentagonal.',
__file__)
except ImportError:
pass
import gf
gf.figureOpen([[(0.5877852439880371, -0.80901700258255),
(0.9510565400123596, 0.30901700258255005), (0, 1.0),
(-0.9510565400123596, 0.30901700258255005),
(-0.5877852439880371, -0.80901700258255)],
[[3, 4], [4, 0], [0, 1], [1, 2], [2, 3]], [[0, 1, 2, 3, 4]]])
try:
import figureInfo
figureInfo.setNameDescPath('Regular Pentagon', None, __file__)
except ImportError:
pass
import gf
gf.figureOpen([[(-0.5773502588272095, -0.5773502588272095, -0.5773502588272095), (-0.5773502588272095, -0.5773502588272095, 0.5773502588272095), (-0.5773502588272095, 0.5773502588272095, -0.5773502588272095), (-0.5773502588272095, 0.5773502588272095, 0.5773502588272095), (0.5773502588272095, -0.5773502588272095, -0.5773502588272095), (0.5773502588272095, -0.5773502588272095, 0.5773502588272095), (0.5773502588272095, 0.5773502588272095, -0.5773502588272095), (0.5773502588272095, 0.5773502588272095, 0.5773502588272095), (0.0, 0.35682210326194763, 0.9341723322868347), (0.35682210326194763, 0.9341723322868347, 0.0), (0.9341723322868347, 0.0, 0.35682210326194763), (0.0, 0.35682210326194763, -0.9341723322868347), (0.35682210326194763, -0.9341723322868347, 0.0), (-0.9341723322868347, 0.0, 0.35682210326194763), (0.0, -0.35682210326194763, 0.9341723322868347), (-0.35682210326194763, 0.9341723322868347, 0.0), (0.9341723322868347, 0.0, -0.35682210326194763), (0.0, -0.35682210326194763, -0.9341723322868347), (-0.35682210326194763, -0.9341723322868347, 0.0), (-0.9341723322868347, 0.0, -0.35682210326194763)], [[5, 10], [5, 14], [8, 14], [7, 10], [7, 8], [2, 11], [2, 15], [9, 15], [6, 11], [6, 9], [4, 12], [4, 16], [10, 16], [5, 12], [6, 16], [7, 9], [4, 17], [11, 17], [0, 17], [0, 18], [12, 18], [1, 14], [1, 18], [0, 19], [2, 19], [13, 19], [1, 13], [8, 3], [13, 3], [15, 3]], [[0, 3, 4, 2, 1], [5, 8, 9, 7, 6], [10, 13, 0, 12, 11], [3, 15, 9, 14, 12], [11, 14, 8, 17, 16], [18, 16, 10, 20, 19], [21, 1, 13, 20, 22], [23, 18, 17, 5, 24], [19, 22, 26, 25, 23], [27, 2, 21, 26, 28], [7, 15, 4, 27, 29], [28, 25, 24, 6, 29]], [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]]])
try:
import figureInfo
figureInfo.setNameDescPath('Regular Dodecahedron', 'One of the five Platonic Solids (regular polyhedra).\nIts faces are pentagonal.', __file__)
except ImportError: pass
import gf
gf.figureOpen([[(-1.0, 0.0, 0.0, 0.0), (0.0, -1.0, 0.0, 0.0), (0.0, 0.0, -1.0, 0.0), (0.0, 0.0, 0.0, -1.0), (1.0, 0.0, 0.0, 0.0), (0.0, 1.0, 0.0, 0.0), (0.0, 0.0, 1.0, 0.0), (0.0, 0.0, 0.0, 1.0)], [[0, 1], [0, 2], [1, 2], [0, 3], [1, 3], [2, 3], [1, 4], [2, 4], [3, 4], [0, 5], [2, 5], [3, 5], [4, 5], [1, 6], [3, 6], [4, 6], [0, 6], [5, 6], [0, 7], [1, 7], [6, 7], [4, 7], [5, 7], [2, 7]], [[0, 2, 1], [0, 4, 3], [1, 5, 3], [2, 5, 4], [2, 7, 6], [4, 8, 6], [5, 8, 7], [1, 10, 9], [3, 11, 9], [5, 11, 10], [7, 12, 10], [8, 12, 11], [4, 14, 13], [6, 15, 13], [8, 15, 14], [3, 14, 16], [9, 17, 16], [11, 17, 14], [12, 17, 15], [0, 13, 16], [0, 19, 18], [16, 20, 18], [13, 20, 19], [6, 21, 19], [15, 20, 21], [9, 22, 18], [17, 20, 22], [12, 22, 21], [2, 23, 19], [7, 21, 23], [1, 23, 18], [10, 22, 23]], [[0, 1, 2, 3], [3, 4, 5, 6], [2, 7, 8, 9], [6, 9, 10, 11], [5, 12, 13, 14], [8, 15, 16, 17], [11, 14, 17, 18], [1, 19, 15, 12], [19, 20, 21, 22], [13, 23, 22, 24], [16, 25, 21, 26], [18, 27, 24, 26], [4, 28, 23, 29], [7, 30, 25, 31], [10, 29, 31, 27], [0, 20, 30, 28]], [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]]])
try:
import figureInfo
figureInfo.setNameDescPath('Regular hexadecachoron', '4-dimensional octahedron (4-orthoplex).\nOne of the six regular polychora (4-dimensional analogy of Platonic solids).\nIts cells are tetrahedral.', __file__)
except ImportError: pass
(0.5, -0.5, 0.5, -0.5), (0.5, -0.5, 0.5, 0.5),
(0.5, 0.5, -0.5, -0.5), (0.5, 0.5, -0.5, 0.5),
(0.5, 0.5, 0.5, -0.5), (0.5, 0.5, 0.5, 0.5)],
[[12, 13], [12, 14], [13, 15], [14, 15], [9, 11], [9, 13],
[11, 15], [10, 11], [10, 14], [8, 10], [8, 12], [8, 9], [1, 9],
[1, 3], [11, 3], [0, 1], [0, 8], [2, 10], [2, 3], [0, 2],
[1, 5], [13, 5], [4, 5], [4, 12], [0, 4], [2, 6], [14, 6],
[4, 6], [15, 7], [3, 7], [5, 7], [6, 7]],
[[0, 2, 3, 1], [4, 6, 2, 5], [7, 6, 3, 8], [8, 9, 10, 1],
[5, 11, 10, 0], [4, 11, 9, 7], [12, 13, 14, 4],
[15, 12, 11, 16], [17, 18, 14, 7], [15, 13, 18, 19],
[19, 17, 9, 16], [12, 20, 21, 5], [22, 23, 0, 21],
[15, 20, 22, 24], [24, 23, 10, 16], [17, 25, 26, 8],
[23, 27, 26, 1], [19, 25, 27, 24], [28, 6, 14, 29],
[2, 28, 30, 21], [13, 29, 30, 20], [3, 28, 31, 26],
[18, 29, 31, 25], [22, 30, 31, 27]],
[[0, 1, 2, 3, 4, 5], [6, 7, 8, 5, 9, 10],
[11, 12, 7, 4, 13, 14], [15, 10, 16, 3, 17, 14],
[1, 18, 19, 20, 6, 11], [2, 18, 21, 22, 8, 15],
[21, 19, 23, 12, 0, 16], [9, 20, 22, 23, 13, 17]],
[[0, 1, 2, 3, 4, 5, 6, 7]]])
try:
import figureInfo
figureInfo.setNameDescPath(
'Tesseract',
'4-dimensional cube (4-cube).\nOne of the six regular polychora (4-dimensional analogy of Platonic solids).\nIts cells are cubical.',
__file__)
except ImportError:
pass
import gf
import math
gf.figureOpen([
[
(math.sqrt(3)/2, -0.5),
(0, 1.0),
(-math.sqrt(3)/2, -0.5)
], [[2, 0], [0, 1], [1, 2]], [[0, 1, 2]]])
try:
import figureInfo
figureInfo.setNameDescPath('Regular Triangle', '2-simplex.', __file__)
except ImportError: pass