| Type: | Near-miss Johnson solid Symmetrohedron |
| Faces: | 74: 6 hexagons 12 pentagons 8+24+24 non-equilateral triangles |
| Edges: | 132 |
| Vertices: | 60 |
| Symmetry: | order 24 |
| Rotation Group: | order 12 |
| Properties: | convex |
| Net: | Pyritohedral_near-miss_johnson-net.png |
In geometry, a pentahexagonal pyritoheptacontatetrahedron is a near-miss Johnson solid with pyritohedral symmetry. This near-miss was discovered by Mason Green in 2006. It has 6 hexagonal faces, 12 pentagonal faces, and 56 triangles in 3 symmetry positions. Mason calls it a hexagonally expanded snubbed dodecahedron.[1]
With regular hexagons and pentagons it is a symmetrohedron.[2] The triangles are not equilateral, with triangle-triangle edges compressed by 1.8%.
It has 3 vertex configurations, 3.3.5.6, 3.5.3.6, 3.3.3.3.5, with the last shared in the snub dodecahedron.