Simplest Canonical Polyhedra of Each Symmetry Type
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Simplest Canonical Polyhedron with D8h Symmetry
(Octagonal Dipyramid)
(1 of 2)
Vertices:
10 (8[4] + 2[8])
Faces:
16 (isosceles triangles)
Edges:
24 (8 short + 16 long)
Symmetry:
8-fold Prismatic (D8h)
Dihedral Angle:
acos(−(7+4*sqrt(2))/17)
≈138.117959056 degrees
Dual Solid:
Simplest D8h (2 of 2)
(values below based on edge-scribed radius = 1)
Short Edge (8):
2*sqrt(2)−2
≈0.82842712474619009760
Long Edge (16):
2*sqrt(2)
≈2.8284271247461900976
[4]-Vertex Radius (8):
sqrt(2*(2−sqrt(2)))
≈1.0823922002923939688
[8]-Vertex Radius (2):
sqrt(2*(2+sqrt(2)))
≈2.6131259297527530557
Edge-scribed Radius:
1
Inscribed Radius:
sqrt(34*(6+sqrt(2)))/17
≈0.93394883109446475958
Volume:
16*sqrt(2*(2−sqrt(2)))/3
≈5.7727584015594345003