# 10 10 duoprism

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In geometry of 4 dimensions, a 10-10 duoprism is a polygonal duoprism, a 4-polytope resulting from the Cartesian product of two decagons.

## Contents

It has 100 vertices, 200 edges, 120 faces (100 squares, and 20 decagons), in 20 decagonal prism cells. It has Coxeter diagram , and symmetry [[10,2,10]], order 800.

## Images

The uniform 10-10 duoprism can be constructed from [10]×[10] or [5]×[5] symmetry, order 400 or 100, with extended symmetry doubling these with a 2-fold rotation that maps the two orientations of prisms together.

The regular complex polytope 10{4}2, , in C 2 has a real representation as a 10-10 duoprism in 4-dimensional space. 10{4}2 has 100 vertices, and 20 10-edges. Its symmetry is 10[4]2, order 200.

It also has a lower symmetry construction, , or 10{}×10{}, with symmetry 10[2]10, order 100. This is the symmetry if the red and blue 10-edges are considered distinct.

## 10-10 duopyramid

The dual of a 10-10 duoprism is called a 10-10 duopyramid. It has 100 tetragonal disphenoid cells, 200 triangular faces, 120 edges, and 20 vertices.

Orthogonal projection

The regular complex polygon 2{4}10 has 20 vertices in C 2 with a real representation in R 4 matching the same vertex arrangement of the 10-10 duopyramid. It has 100 2-edges corresponding to the connecting edges of the 10-10 duopyramid, while the 20 edges connecting the two decagons are not included.

The vertices and edges makes a complete bipartite graph with each vertex from one decagon is connected to every vertex on the other.

## References

10-10 duoprism Wikipedia