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The order-5 truncated pentagonal hexecontahedron is a convex polyhedron with 72 faces: 60 hexagons and 12 pentagons triangular, with 210
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Its topology can be constructed in Conway polyhedron notation as ''t5gD'' and more simply ''wD'' as a ''whirled dodecahedron'', reducing original pentagonal faces and adding 5 distorted hexagons around each, in clockwise or counter-clockwise forms. This picture shows its flat construction before the geometry is adjusted into a more spherical form. The snub can create a (5,3) geodesic polyhedron by k5k6.
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Fourth class of convex equilateral polyhedron with polyhedral symmetry related to fullerenes and viruses
Stan Schein and James Maurice Gaye,
VRML polyhedral generator
Try "t5gI" ( Conway polyhedron notation) Goldberg polyhedra Pentagonal tilings Snub tilings Fullerenes {{polyhedron-stub
edges
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, and 140 vertices. Its dual is the pentakis snub dodecahedron.
It is Goldberg polyhedron 2,1 in the icosahedral family, with chiral symmetry. The relationship between pentagons steps into 2 hexagons away, and then a turn with one more step.
It is a Fullerene C140.
Construction
It is explicitly called a ''pentatruncated pentagonal hexecontahedron'' since only the valence-5 vertices of thepentagonal hexecontahedron
In geometry, a pentagonal hexecontahedron is a Catalan solid, dual of the snub dodecahedron. It has two distinct forms, which are mirror images (or "enantiomorphs") of each other. It has 92 vertices that span 60 pentagonal faces. It is the Catala ...
are truncated.''Shaping Space: Exploring Polyhedra in Nature, Art, and the Geometrical Imagination'', 2013, Chapter 9 ''Goldberg polyhedra'/ref> :
Its topology can be constructed in Conway polyhedron notation as ''t5gD'' and more simply ''wD'' as a ''whirled dodecahedron'', reducing original pentagonal faces and adding 5 distorted hexagons around each, in clockwise or counter-clockwise forms. This picture shows its flat construction before the geometry is adjusted into a more spherical form. The snub can create a (5,3) geodesic polyhedron by k5k6.
:
Related polyhedra
The whirled dodecahedron creates more polyhedra by basic Conway polyhedron notation. The zip whirled dodecahedron makes a chamfered truncated icosahedron, and Goldberg (4,1). Whirl applied twice produces Goldberg (5,3), and applied twice with reverse orientations produces goldberg (7,0).See also
* Truncated pentagonal icositetrahedronbr>t4gCReferences
* * *Fourth class of convex equilateral polyhedron with polyhedral symmetry related to fullerenes and viruses
Stan Schein and James Maurice Gaye,
PNAS
''Proceedings of the National Academy of Sciences of the United States of America'' (often abbreviated ''PNAS'' or ''PNAS USA'') is a peer-reviewed multidisciplinary scientific journal. It is the official journal of the National Academy of Scien ...
, Early Edition doi: 10.1073/pnas.1310939111
External links
VRML polyhedral generator
Try "t5gI" ( Conway polyhedron notation) Goldberg polyhedra Pentagonal tilings Snub tilings Fullerenes {{polyhedron-stub