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. Net. <BR>Net