Pentahexagonal pyritoheptacontatetrahedron

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.

With regular hexagons and pentagons it is a symmetrohedron. 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.

• Tetrated dodecahedron has tetrahedral symmetry

• Near Misses Archived 2012-07-16 at the Wayback Machine
• 24 Johnson Solid Near Misses