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 C4v Symmetry
(Square Pyramid)
Vertices:
5 (4[3] + 1[4])
Faces:
5 (4 isosceles triangles + 1 square)
Edges:
8 (4 short + 4 long)
Symmetry:
4-fold Pyramidal (C4v)
Dual Solid:
Square Pyramid (itself)
(values below based on edge-scribed radius = 1)
Short Edge (4):
2*sqrt(2*(sqrt(2)−1))
≈1.8203594422489093652
Long Edge (4):
2*sqrt(1+sqrt(2))
≈3.1075479480600746147
Edge-scribed Radius:
1
Volume:
16*(2−sqrt(2))/3
≈3.1241943340101597397