A solid has 20 vertices of degree six and 12 vertices of deg

A solid has 20 vertices of degree six and 12 vertices of degree five. How many faces does it have? Explain your answer.

Solution

the solid totally has 32 vertices and is called catalan solid

It has 30 faces, 60 edges and 32 vertices.It is dualbpolyhedron of icosidodecahedron.

The 32 vertices are again divided has 20nvertices with degree6 and 12 vvertices with degree 5.

it satisfies eulers formula where

V-E+F = 2 implies

32-60+30=2