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Input interpretation:

regular icosahedron  |  truncated icosahedron


Visual representations:



Combinatorial properties:

 | vertices | edges | faces\nregular icosahedron | 12 | 30 | 20  (20 triangles)\ntruncated icosahedron | 60 | 90 | 32  (12 pentagons, 20 hexagons)


Geometric properties:

 | regular icosahedron | truncated icosahedron\nvolume | (5 phi^2)\/6 | 1\/4 (125 + 43 sqrt(5))\nsurface area | 5 sqrt(3) | 3 sqrt(5 (65 + 2 sqrt(5) + 4 sqrt(75 + 30 sqrt(5))))\ncircumradius | 1\/4 sqrt(10 + 2 sqrt(5)) | 1\/4 sqrt(58 + 18 sqrt(5))\nmidradius | phi\/2 | (3 phi)\/2\ninradius | 1\/12 (3 sqrt(3) + sqrt(15)) | \n(assuming unit edge lengths)


Schläfli symbol:

 | regular icosahedron | truncated icosahedron\nSchläfli symbol | {3, 5} | t{3, 5}

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