Simplest Canonical Polyhedra of Each Symmetry Type
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(F: faces)
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Simplest Canonical Polyhedron with C2h Symmetry
(2 of 2)
Vertices:
10 (4[3] + 4[3] + 2[4])
Faces:
8 (2 isosceles triangles + {2 opposite * 2} irregular tetragons
+ 2 mirror-symmetric pentagons)
Edges:
16 (5 different lengths)
Symmetry:
2-fold Cyclic + Perpendicular Reflection (C2h)
Dual Solid:
Simplest C2h (1 of 2)
(values below based on edge-scribed radius = 1)
Edge 1 (2):
3−sqrt(5)
≈0.76393202250021030359
Edge 2 (4):
1
Edge 3 (2):
sqrt(5)−1
≈1.2360679774997896964
Edge 4 (4):
(5−sqrt(5))/2
≈1.3819660112501051518
Edge 5 (4):
(1+sqrt(5))/2
≈1.6180339887498948482
Edge-scribed Radius:
1
Volume:
2*sqrt(2*(13*sqrt(5)−19))/3
≈2.99167492403648042749