Simplest Canonical Polyhedra of Each Symmetry Type
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(F: faces)
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Simplest Canonical Polyhedron with Th Symmetry
(2 of 2)
Vertices:
20 (12[3] + 8[6])
Faces:
24 (12 isosceles triangles + 12 isosceles trapezoids)
Edges:
42 (6 short + 24 medium + 12 long)
Symmetry:
Pyritohedral (Th)
Dual Solid:
Simplest Th (1 of 2)
(values below based on edge-scribed radius = 1)
Short Edge (6):
sqrt(2)−1
≈0.41421356237309504880
Medium Edge (24):
(2*sqrt(2)−1)/2
≈0.91421356237309504880
Long Edge (12):
sqrt(2)
≈1.4142135623730950488
Edge-scribed Radius:
1
Volume:
7−2*sqrt(2)
≈4.1715728752538099024