Simplest Canonical Polyhedra of Each Symmetry Type
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Simplest Canonical Polyhedron with D6v Symmetry
(Hexagonal Antiprism)
(1 of 2)
Vertices:
12 (12[4])
Faces:
14 (12 equilateral triangles + 2 regular hexagons)
Edges:
24 (all same length)
Symmetry:
6-fold Antiprismatic (D6v)
Hexagon-Triangle Angle:
acos(−(2*sqrt(3)−3)/3)
≈98.899428880 degrees
Triangle-Triangle Angle:
acos(−(2*sqrt(3)−1)/3)
≈145.221891332 degrees
Dual Solid:
Simplest D6v (2 of 2)
(values below based on midscribed radius = 1)
Edge Length:
2*sqrt(2−sqrt(3))
≈1.0352761804100830494
Circumscribed Radius:
sqrt(3−sqrt(3))
≈1.1260325006104942380
Midscribed Radius:
1
Hexagon Center Radius:
sqrt(3*sqrt(3)−5)
≈0.44289098286895826186
Triangle Center Radius:
sqrt(3*(1+sqrt(3)))/3
≈0.95429743923106023278
Volume:
8*sqrt(2*(11*sqrt(3)−19))
≈2.5937496133935575561