What makes a solid perfect? What are the possible faces of the Platonic solids? Solution Pefrect solid has two properties 1. each face is the same regular polygon and 2. Same number of polygons meet at each vertex (corner) Possile faces : Tetrahedron : 4 triangular faces Cube : 6 square faces Octahendram : 8 triangles face Dodecahedron : 12 pentagon faces Icosahedron : 20 triangular faces.