Simplest Canonical Polyhedra of Each Symmetry Type
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(F: faces)
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Simplest Canonical Polyhedron with
Ci = S2
Symmetry
Vertices:
10 (6[3] + 2[4] + 2[5])
Faces:
10 ({2 opposite * 3} scalene triangles
+ 2 opposite irregular tetragons
+ 2 opposite irregular pentagons)
Edges:
18 (8 different lengths)
Symmetry:
Inversion (Ci = S2)
Dual Solid:
Simplest Ci (itself)
(values below based on edge-scribed radius = 1)
Edge 1 (2):
sqrt(sqrt(2))/2
≈0.59460355750136053336
Edge 2 (2):
sqrt(2*sqrt(2))/2
≈0.84089641525371454303
Edge 3 (2):
sqrt(9*sqrt(2)−8)/2
≈1.0871892730060685527
Edge 4 (2):
sqrt(2*(11*sqrt(2)−12))/2
≈1.3334821307584225624
Edge 5 (2):
sqrt(4+3*sqrt(2))/2
≈1.4354999727550750764
Edge 6 (2):
sqrt(2*(9*sqrt(2)−8))/2
≈1.5375178147517275904
Edge 7 (2):
sqrt(2*sqrt(2))
≈1.6817928305074290861
Edge 8 (4):
sqrt(2*(4+3*sqrt(2)))/2
≈2.0301035302564356097
Edge-scribed Radius:
1
Volume:
2*(5*sqrt(2)−2)/3
≈3.3807118745769834960