Pentahexagonal_pyritoheptacontatetrahedron

Pentahexagonal pyritoheptacontatetrahedron

Pentahexagonal pyritoheptacontatetrahedron

Near-miss Johnson solid with 74 faces

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]

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Model built with polydron

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.

See also

References

  1. [1]
    Near Misses based on dodecahedra
  2. [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).
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