Claim: As a polyhedral compound with identical uniform polyhedra, the three tetrahedra has twelve faces.
Evidence: There are five regular compounds of polyhedra: Two tetrahedra
{4,3}[2{3,3}]{3,4} Five tetrahedra
{5,3}[5{3,3}]{3,5} Ten tetrahedra
2{5,3}[10{3,3}]2{3,5} Two tetrahedra Ten tetrahedra Faces by sides 4{3} Tetrahedron name Regular tetrahedron Triangular pyramid Mirrored sphenoid Irregular tetrahedron
(No symmetry) Tetragonal disphenoid Rhombic disphenoid Digonal disphenoid Phyllic disphenoid The naming system is based on Classical Greek, for example tetrahedron (a polyhedron with four faces), pentahedron (five faces), hexahedron (six faces), triacontahedron (30 faces), and so on.