Simplest Canonical Polyhedra of Each Symmetry Type

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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