Simplest Canonical Polyhedra of Each Symmetry Type
(box: x-ray)
(F: faces)
(slider: perspective)
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(M: metrics)
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Simplest Canonical Polyhedron with C2h Symmetry
(1 of 2)
Vertices:
8 (2[3] + 4[4] + 2[5])
Faces:
10 (4 isosceles triangles + {2 opposite * 2} obtuse triangles + 2 kites)
Edges:
16 (4 short + 4 medium + 8 long)
Symmetry:
2-fold Cyclic + Perpendicular Reflection (C2h)
Dual Solid:
Simplest C2h (2 of 2)
(values below based on edge-scribed radius = 1)
Short Edge (4):
sqrt(5*(sqrt(5)−2))
≈1.0864344837582008940
Medium Edge (4):
sqrt(2*(sqrt(5)−1))
≈1.5723027555148465721
Long Edge (8):
sqrt(2+sqrt(5))
≈2.0581710272714922503
Edge-scribed Radius:
1
Volume:
2*sqrt(10*(1+sqrt(5)))/3
≈3.7924298733718873819