Simplest Canonical Polyhedra of Each Symmetry Type

(box: x-ray)  (F: faces)  (slider: perspective)  (image: L=rotate R=zoom)  (M: metrics)
Please use a browser that supports "canvas"

Simplest Canonical Polyhedron with C7v Symmetry
(Heptagonal Pyramid)
Vertices:  8  (7[3] + 1[7])
Faces:8  (7 isosceles triangles + 1 regular heptagon)
Edges:14  (7 short + 7 long)
Symmetry:  7-fold Pyramidal  (C7v)
Dual Solid:  Heptagonal Pyramid (itself)
(values below based on edge-scribed radius = 1)
Short Edge (7):  sqrt(root[(x^3)−8*(x^2)−576*x+512])    ≈0.93772603323035618000
Long Edge (7):  sqrt(root[(x^3)−32*(x^2)+192*x+512])    ≈4.7345012288982147881
Edge-scribed Radius:  1
Volume:root[27*(x^3)−1008*(x^2)+9408*x−25088]    ≈4.9097770568078728097