Simplest Canonical Polyhedra of Each Symmetry Type
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Simplest Canonical Polyhedron with D4v Symmetry
(Square Antiprism)
(1 of 2)
Vertices:
8 (8[4])
Faces:
10 (8 equilateral triangles + 2 squares)
Edges:
16 (all same length)
Symmetry:
4-fold Antiprismatic (D4v)
Square-Triangle Angle:
acos(−(sqrt(6)−sqrt(3))/3)
≈103.836160479 degrees
Triangle-Triangle Angle:
acos(−(2*sqrt(2)−1)/3)
≈127.551602906 degrees
Dual Solid:
Simplest D4v (2 of 2)
(values below based on midscribed radius = 1)
Edge Length:
2*sqrt(2−sqrt(2))
≈1.5307337294603590869
Circumscribed Radius:
sqrt(3−sqrt(2))
≈1.2592801267497652967
Midscribed Radius:
1
Square Center Radius:
sqrt(sqrt(2)−1)
≈0.64359425290558262474
Triangle Center Radius:
sqrt(3*(1+sqrt(2)))/3
≈0.89707182216607663118
Volume:
16*sqrt(sqrt(2)−1)/3
≈3.4325026821631073319