Simplest Canonical Polyhedra of Each Symmetry Type
(box: x-ray)
(F: faces)
(slider: perspective)
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(M: metrics)
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Simplest Canonical Polyhedron with C5v Symmetry
(Pentagonal Pyramid)
Vertices:
6 (5[3] + 1[5])
Faces:
6 (5 isosceles triangles + 1 regular pentagon)
Edges:
10 (5 short + 5 long)
Symmetry:
5-fold Pyramidal (C5v)
Dual Solid:
Pentagonal Pyramid (itself)
(values below based on edge-scribed radius = 1)
Short Edge (5):
2*sqrt(2*(sqrt(5)−2))
≈1.3742429988900498566
Long Edge (5):
2*sqrt(1+sqrt(5))
≈3.59781487989573454452
Edge-scribed Radius:
1
Volume:
4*(5−sqrt(5))/3
≈3.685242696666947071454