Simplest Canonical Polyhedra of Each Symmetry Type
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Simplest Canonical Polyhedron with D10h Symmetry
(Decagonal Prism)
(2 of 2)
Vertices:
20 (20[3])
Faces:
12 (10 squares + 2 regular decagons)
Edges:
30 (all same length)
Symmetry:
10-fold Prismatic (D10h)
Decagon-Square Angle:
acos(0)
90 degrees
Square-Square Angle:
acos(−(1+sqrt(5))/4)
144 degrees
Dual Solid:
Simplest D10h (1 of 2)
(values below based on midscribed radius = 1)
Edge Length:
(sqrt(5)−1)/2
≈0.61803398874989484820
Circumscribed Radius:
sqrt(2*(11−sqrt(5)))/4
≈1.04665729960313480248
Midscribed Radius:
1
Decagon Center Radius:
(sqrt(5)−1)/4
≈0.30901699437494742410
Square Center Radius:
sqrt(2*(5+sqrt(5)))/4
≈0.95105651629515357212
Volume:
5*sqrt(5−2*sqrt(5))/2
≈1.8163563200134022147