Pentahexagonal pyritoheptacontatetrahedron

From Wikipedia, the free encyclopedia
Pentahexagonal pyritoheptacontatetrahedron
Pyritohedral near-miss johnson.png
Faces 74:
6 hexagons
12 pentagons
8+24+24 triangles
Edges 132
Vertices 60
Symmetry group Th, [3+,4], (3*2), order 24
Rotation group T, [3,3]+, (332), order 12
Properties convex
Model built with polydron

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.

Net[]

Pyritohedral near-miss johnson-net.png
Net

See also[]

References[]

  1. ^ Near Misses based on dodecahedra
  2. ^ Kaplan, Craig S.; Hart, George W. (2001), "Symmetrohedra: Polyhedra from Symmetric Placement of Regular Polygons", Bridges: Mathematical Connections in Art, Music and Science (PDF).

External links[]

Retrieved from ""