Question

It is the solid that results from the intersection of a dodecahedron and an icosahedron of a specific relative scale. Its faces comprise 12 regular pentagons and 20 equilateral triangles, all of the same edge length. If the edge length is 1 then find the volume of the polyhedron.
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Answer 1

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Type Platonic solid

Elements F = 20, E = 30

V = 12 (χ = 2)

Faces by sides 20{3}

Conway notation IsT

Schläfli symbols {3,5}s{3,4}

sr{3,3} or displaystyle

Face configuration V5.5.5

Wythoff symbol 5 | 2 3

Coxeter diagram CDel node.pngCDel 5.pngCDel node.pngCDel 3.pngCDel node 1.png

Symmetry Ih, H3, [5,3], (*532)

Rotation group I, [5,3]+, (532)

Answer 2

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