REGULAR CONVEX POLYHEDRONS  - Common Properties - One Family

 *(p,q) Vertices (v) Edges (e) Faces (f) Vertex angle (α) θ) Inradius (r) Circumradius (R) R/r Surface area (A) Volume (V) P l a t o n i c    s o l i d s tetrahedron (3,3) 4 6 4 60° 70.53° 3 cube (4,3) 8 12 6 90° 90° octahedron (3,4) 6 12 8 60° 109.47° dodecahedron (5,3) 20 30 12 108° 116.57° ≈ 1,25841 icosahedron (3,5) 12 30 20 60° 138.19° ≈ 1,25841 S p h e r i c a  l     p o l y h e d r o n s dihedrons (2,n) 2 2…n 2…n 360°/n 180° r r 1 Platonic spheres tetrahedral (3,3) 4 6 4 120° octahedral (3,4) 6 12 8 90° hexahedral (4,3) 8 12 6 120° dodecahedral (5,3) 20 30 12 120° icosahedral (3,5) 12 30 20 72°
* the number of edges in a face,  q the number of edges meeting at a vertex

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(3)                                 v + f - e = 2           Euler's formula

(4)                           fp = vq = 2e

By mirco
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