Pentagonal hexecontahedron
Encyclopedia
In geometry
, a pentagonal hexecontahedron is a Catalan solid
, dual of the snub dodecahedron
. It has two distinct forms, which are mirror image
s (or "enantiomorph
s") of each other. It is also well-known to be the Catalan Solid with the most vertices. Among the Catalan and Archimedian solids, it has the second largest amount of vertices, after the Truncated icosidodecahedron
, which has 120 vertices.
s (V3.3.3.3.n). (The sequence progresses into tilings the hyperbolic plane to any n.) These face-transitive figures have (n32) rotational symmetry.
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, a pentagonal hexecontahedron is a Catalan solid
Catalan solid
In mathematics, a Catalan solid, or Archimedean dual, is a dual polyhedron to an Archimedean solid. The Catalan solids are named for the Belgian mathematician, Eugène Catalan, who first described them in 1865....
, dual of the snub dodecahedron
Snub dodecahedron
In geometry, the snub dodecahedron, or snub icosidodecahedron, is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed by two or more types of regular polygon faces....
. It has two distinct forms, which are mirror image
Mirror image
A mirror image is a reflected duplication of an object that appears identical but reversed. As an optical effect it results from reflection off of substances such as a mirror or water. It is also a concept in geometry and can be used as a conceptualization process for 3-D structures...
s (or "enantiomorph
Chirality (mathematics)
In geometry, a figure is chiral if it is not identical to its mirror image, or, more precisely, if it cannot be mapped to its mirror image by rotations and translations alone. For example, a right shoe is different from a left shoe, and clockwise is different from counterclockwise.A chiral object...
s") of each other. It is also well-known to be the Catalan Solid with the most vertices. Among the Catalan and Archimedian solids, it has the second largest amount of vertices, after the Truncated icosidodecahedron
Truncated icosidodecahedron
In geometry, the truncated icosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed by two or more types of regular polygon faces....
, which has 120 vertices.
Related polyhedra and tilings
This polyhedron is topologically related as a part of sequence of polyhedra and tilings of pentagons with face configurationFace configuration
In geometry, a face configuration is notational description of a face-transitive polyhedron. It represents a sequential count of the number of faces that exist at each vertex around a face....
s (V3.3.3.3.n). (The sequence progresses into tilings the hyperbolic plane to any n.) These face-transitive figures have (n32) rotational symmetry.
 V3.3.3.3.3 (332) and (532) |
 V3.3.3.3.4 Pentagonal icositetrahedron In geometry, a pentagonal icositetrahedron is a Catalan solid which is the dual of the snub cube. It has two distinct forms, which are mirror images of each other.... (432) |
 V3.3.3.3.5 Pentagonal hexecontahedron In geometry, a pentagonal hexecontahedron is a Catalan solid, dual of the snub dodecahedron. It has two distinct forms, which are mirror images of each other. It is also well-known to be the Catalan Solid with the most vertices... (532) |
 V3.3.3.3.6 (632) |
 V3.3.3.3.7 (732) |
External links
- Pentagonal Hexecontrahedron -- Interactive Polyhedron Model