Simplest Canonical Polyhedra of Each Symmetry Type
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Simplest Canonical Polyhedron with D5v Symmetry
(Pentagonal Antiprism)
(1 of 2)
Vertices:
10 (10[4])
Faces:
12 (10 equilateral triangles + 2 regular pentagons)
Edges:
20 (all same length)
Symmetry:
5-fold Antiprismatic (D5v)
Pentagon-Triangle Angle:
acos(−sqrt(15*(5−2*sqrt(5)))/15)
≈100.812316964 degrees
Triangle-Triangle Angle:
acos(−sqrt(5)/3)
≈138.189685104 degrees
Dual Solid:
Simplest D5v (2 of 2)
(values below based on midscribed radius = 1)
Edge Length:
sqrt(5)−1
≈1.2360679774997896964
Circumscribed Radius:
sqrt(2*(5−sqrt(5)))/2
≈1.1755705045849462583
Midscribed Radius:
1
Pentagon Center Radius:
sqrt(10*(5−sqrt(5)))/10
≈0.52573111211913360603
Triangle Center Radius:
(sqrt(3)+sqrt(15))/6
≈0.934172358962715696451
Volume:
4*sqrt(5)/3
≈2.9814239699997195952