Regular deltahedra Image Name Faces Edges Vertices Vertex configurations Symmetry group tetrahedron 4 6 4 4 × 33 Td, [3,3] octahedron 8 12 6 6 × 34 Oh, [4,3] icosahedron 20 30 12 12 × 35 Ih, [5,3] Johnson deltahedra Image Name Faces Edges Vertices Vertex configurations Symmetry group triangular bipyramid 6 9 5 2 × 33 3 × 34 D3h, [3,2] pentagonal bipyramid 10 15 7 5 × 34 2 × 35 D5h, [5,2] snub disphenoid 12 18 8 4 × 34 4 × 35 D2d, [2,2] triaugmented triangular prism 14 21 9 3 × 34 6 × 35 D3h, [3,2] gyroelongated square bipyramid 16 24 10 2 × 34 8 × 35 D4d, [4,2]