Simplest Canonical Polyhedra of Each Symmetry Type
(box: x-ray)
(F: faces)
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Simplest Canonical Polyhedron with Th Symmetry
(1 of 2)
Vertices:
24 (12[3] + 12[4])
Faces:
20 (12 isosceles triangles + 8 triambi)
Edges:
42 (36 short + 6 long)
Symmetry:
Pyritohedral (Th)
Dual Solid:
Simplest Th (2 of 2)
(values below based on edge-scribed radius = 1)
Short Edge (36):
(9*sqrt(2)−8)/7
≈0.67541743733683649132
Long Edge (6):
2*(sqrt(2)−1)
≈0.82842712474619009760
Edge-scribed Radius:
1
Volume:
8*(33−17*sqrt(2))/21
≈3.4127121674885273030