Triangular hebesphenorotunda

Infobox Polyhedron with net

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Polyhedron_Type=Johnson
J₉₁ - J₉₂ - J₁
Face_List=1+2x3+6 triangles
3 squares
3 pentagons
1 hexagon
Edge_Count=36
Vertex_Count=18
Symmetry_Group="C"_3v
Vertex_List= 3(3³.5)
6(3.4.3.5)
3(3.5.3.5)
2.3(3².4.6)
Dual=-
Property_List=convex
Net_

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In geometry, the triangular hebesphenorotunda is one of the Johnson solids ("J"₉₂). 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.

External links

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** mathworld | urlname = TriangularHebesphenorotunda| title = Triangular hebesphenorotunda