Triangular hebesphenorotunda
Encyclopedia
In geometry
, the triangular hebesphenorotunda is one of the Johnson solid
s (J92). It is one of the elementary Johnson solids, which do not arise from "cut and paste" manipulations of the Platonic
and Archimedean
solids. However, it does have a strong relationship to the icosidodecahedron
, an Archimedean solid. Most evident is the cluster of three pentagons and four triangles on one side of the solid. If these faces are aligned with a congruent patch of faces on the icosidodecahedron, then the hexagonal face will lie in the plane midway between two opposing triangular faces of the icosidodecahedron.
The triangular hebesphenorotunda is the only Johnson solid with faces of 3, 4, 5 and 6 sides. The 92 Johnson solids were named and described by Norman Johnson in 1966.
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 ....
, the triangular hebesphenorotunda is one of the Johnson solid
Johnson solid
In geometry, a Johnson solid is a strictly convex polyhedron, each face of which is a regular polygon, but which is not uniform, i.e., not a Platonic solid, Archimedean solid, prism or antiprism. There is no requirement that each face must be the same polygon, or that the same polygons join around...
s (J92). It is one of the elementary Johnson solids, which do not arise from "cut and paste" manipulations of the Platonic
Platonic solid
In geometry, a Platonic solid is a convex polyhedron that is regular, in the sense of a regular polygon. Specifically, the faces of a Platonic solid are congruent regular polygons, with the same number of faces meeting at each vertex; thus, all its edges are congruent, as are its vertices and...
and Archimedean
Archimedean solid
In geometry an Archimedean solid is a highly symmetric, semi-regular convex polyhedron composed of two or more types of regular polygons meeting in identical vertices...
solids. However, it does have a strong relationship to the icosidodecahedron
Icosidodecahedron
In geometry, an icosidodecahedron is a polyhedron with twenty triangular faces and twelve pentagonal faces. An icosidodecahedron has 30 identical vertices, with two triangles and two pentagons meeting at each, and 60 identical edges, each separating a triangle from a pentagon...
, an Archimedean solid. Most evident is the cluster of three pentagons and four triangles on one side of the solid. If these faces are aligned with a congruent patch of faces on the icosidodecahedron, then the hexagonal face will lie in the plane midway between two opposing triangular faces of the icosidodecahedron.
The triangular hebesphenorotunda is the only Johnson solid with faces of 3, 4, 5 and 6 sides. The 92 Johnson solids were named and described by Norman Johnson in 1966.