Triangular Orthobicoupole

In Geometry, the triangular orthobicoupole is one of the solid of Johnson ( J ₂₇). As the name indicates it, it can be built by attaching two triangular cupolas ( J ₃) by their bases. It has a number equal of squares and triangles to each top; nevertheless, it is not regular top.

The triangular orthobicoupole is the first solid of the infinite whole of the orthobicoupoles.

The triangular orthobicoupole has a surface resemblance to the Cuboctaèdre, which would be known under the name of gyrobicoupole triangular in the nomenclature of the solids of Johnson — the difference lies in the two triangular cupolas which compose the triangular orthobicoupole, it are united in such way that the pairs of with dimensions which coincide are the same ones (consequently, " ortho"); the cuboctaèdre is joined in such way that the triangles coincide with the squares and vice versa. Being given a triangular orthobicoupole, a rotation of 60 degrees of a cupola before the junction gives a cuboctaèdre.

The triangular Orthobicoupole lengthened ( J ₃₅), which is built by lengthening of this solid, has a special relation (different) with the rhombicuboctaèdre.

The dual of the triangular orthobicoupole is called a trapézo-rhombic dodecahedron . It has 8 rhombic faces and 4 trapezoidal faces. It is similar to the rhombic Dodécaèdre and both are polyhedrons which can fill space.

The 92 solid of Johnson were named and described by Norman Johnson in 1966.

External bond

solids of Johnson on the site MathWorld

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