Simplest Canonical Polyhedra of Each Symmetry Type
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(F: faces)
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Simplest Canonical Polyhedron with D8h Symmetry
(Octagonal Prism)
(2 of 2)
Vertices:
16 (16[3])
Faces:
10 (8 squares + 2 regular octagons)
Edges:
24 (all same length)
Symmetry:
8-fold Prismatic (D8h)
Octagon-Square Angle:
acos(0)
90 degrees
Square-Square Angle:
acos(−sqrt(2)/2)
135 degrees
Dual Solid:
Simplest D8h (1 of 2)
(values below based on midscribed radius = 1)
Edge Length:
sqrt(2−sqrt(2))
≈0.76536686473017954346
Circumscribed Radius:
sqrt(6−sqrt(2))/2
≈1.0707224707676243767
Midscribed Radius:
1
Octagon Center Radius:
sqrt(2−sqrt(2))/2
≈0.38268343236508977173
Square Center Radius:
sqrt(2+sqrt(2))/2
≈0.92387953251128675613
Volume:
2*sqrt(2*(2−sqrt(2)))
≈2.1647844005847879376