# 6 6 duoprism

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In geometry of 4 dimensions, a 6-6 duoprism is a polygonal duoprism, a 4-polytope resulting from the Cartesian product of two octagons.

## Contents

It has 36 vertices, 72 edges, 48 faces (36 squares, and 12 hexagons), in 12 hexagonal prism cells. It has Coxeter diagram , and symmetry [[6,2,6]], order 288.

## Images

Net

Seen in a skew 2D orthogonal projection, it contains the projected rhombi of the rhombic tiling.

## Related complex polygons

The regular complex polytope 6{4}2, , in C 2 has a real representation as a 6-6 duoprism in 4-dimensional space. 6{4}2 has 36 vertices, and 12 6-edges. Its symmetry is 6[4]2, order 72. It also has a lower symmetry construction, , or 6{}×6{}, with symmetry 6[2]6, order 36. This is the symmetry if the red and blue 6-edges are considered distinct.

## 6-6 duopyramid

The dual of a 6-6 duoprism is called a 6-6 duopyramid. It has 36 tetragonal disphenoid cells, 72 triangular faces, 48 edges, and 12 vertices.

It can be seen in orthogonal projection:

## Related complex polygon

The regular complex polygon 2{4}6 or has 12 vertices in C 2 with a real represention in R 4 matching the same vertex arrangement of the 6-6 duopyramid. It has 36 2-edges corresponding to the connecting edges of the 6-6 duopyramid, while the 12 edges connecting the two hexagons are not included.

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

## References

6-6 duoprism Wikipedia

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