- Triangular orthobicupola
Infobox Polyhedron
Polyhedron_Type=Johnson
"J"26 - J27 - J28
Face_List=2+6triangle s
6 squares
Edge_Count=24
Vertex_Count=12
Symmetry_Group=D3h
Vertex_List=6(32.42)
6(3.4.3.4)
Dual=Trapezo-rhombic dodecahedron
Property_List=convexIn
geometry , the triangular orthobicupola is one of theJohnson solid s ("J"27). As the name suggests, it can be constructed by attaching twotriangular cupola s ("J"3) along their bases. It has an equal number of squares and triangles at each vertex; however, it is notvertex-transitive .The "triangular orthobicupola" is the first in an infinite set of orthobicupolae.
The "triangular orthobicupola" has a superficial resemblance to the
cuboctahedron , which would be known as the "triangular gyrobicupola" in the nomenclature of Johnson solids — the difference is that the two triangular cupolas which make up the triangular orthobicupola are joined so that pairs of matching sides abut (hence, "ortho"); the cuboctahedron is joined so that triangles abut squares and vice versa. Given a triangular orthobicupola, a 60-degree rotation of one cupola before the joining yields a cuboctahedron.The
elongated triangular orthobicupola ("J"35), which is constructed by elongating this solid, has a (different) special relationship with therhombicuboctahedron .The 92 Johnson solids were named and described by
Norman Johnson in1966 .The dual of the "triangular orthobicupola" is called a "trapezoid-rhombic dodecahedron". It has 6 rhombic and 6 trapezoidal faces. It is similar to the
rhombic dodecahedron and both of them are space-filling polyhedra.External links
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