Simplest Canonical Polyhedra of Each Symmetry Type
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Simplest Canonical Polyhedron with D6v Symmetry
(Hexagonal Trapezohedron)
(2 of 2)
Vertices:
14 (12[3] + 2[6])
Faces:
12 (tri-equiangular kites)
Edges:
24 (12 short + 12 long)
Symmetry:
6-fold Antiprismatic (D6v)
Dihedral Angle:
acos(−sqrt(3)/3)
≈125.264389683 degrees
Dual Solid:
Simplest D6v (1 of 2)
(values below based on edge-scribed radius = 1)
Short Edge (12):
sqrt(2*(3*sqrt(3)−5))
≈0.62634243462603087561
Long Edge (12):
sqrt(2*(1+sqrt(3)))
≈2.33754178896073526154
[3]-Vertex Radius (12):
sqrt(6*(sqrt(3)−1))/2
≈1.0478913165750138710
[6]-Vertex Radius (2):
sqrt(2*(5+3*sqrt(3)))/2
≈2.2578919839871250892
Edge-scribed Radius:
1
Inscribed Radius:
sqrt(6*(3+sqrt(3)))/6
≈0.88807383397711526216
Volume:
4*sqrt(2*(sqrt(3)−1))
≈4.8400026696484448729