Simplest Canonical Polyhedra of Each Symmetry Type
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(F: faces)
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Simplest Canonical Polyhedron with D5h Symmetry
(Pentagonal Prism)
(2 of 2)
Vertices:
10 (10[3])
Faces:
7 (5 squares + 2 regular pentagons)
Edges:
15 (all same length)
Symmetry:
5-fold Prismatic (D5h)
Pentagon-Square Angle:
acos(0)
90 degrees
Square-Square Angle:
acos(−(sqrt(5)−1)/4)
108 degrees
Dual Solid:
Simplest D5h (1 of 2)
(values below based on midscribed radius = 1)
Edge Length:
sqrt(2*(5−sqrt(5)))/2
≈1.1755705045849462583
Circumscribed Radius:
sqrt(2*(13−sqrt(5)))/4
≈1.1599532330281795839
Midscribed Radius:
1
Pentagon Center Radius:
sqrt(2*(5−sqrt(5)))/4
≈0.58778525229247312917
Square Center Radius:
(1+sqrt(5))/4
≈0.80901699437494742410
Volume:
5*sqrt(5)/4
≈2.79508497187473712051