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.Near Misses based on dodecahedra
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.
Dual Polyhedron The dual of the pentahexagonal pyritoheptacontatetrahedron is made of kites, quadrilaterals, and pentagonal faces. It has 60 faces. ImageAnimation
See also Tetrated dodecahedron has tetrahedral symmetry
References
External links Near Misses 24 Johnson Solid Near Misses