8 8 duoprism

Images

The uniform 8-8 duoprism can be constructed from [8]×[8] or [4]×[4] symmetry, order 256 or 64, with extended symmetry doubling these with a 2-fold rotation that maps the two orientations of prisms together. These can be expressed by 4 permutations of uniform coloring of the octahedral prism cells.

Seen in a skew 2D orthogonal projection, it has the same vertex positions as the hexicated 7-simplex, except for a center vertex. The projected rhombi and squares are also shown in the Ammann–Beenker tiling.

Related complex polygons

The regular complex polytope ₈{4}₂, , in C 2 has a real representation as a 8-8 duoprism in 4-dimensional space. ₈{4}₂ has 64 vertices, and 16 8-edges. Its symmetry is ₈[4]₂, order 128.

It also has a lower symmetry construction, , or ₈{}×₈{}, with symmetry ₈[2]₈, order 64. This is the symmetry if the red and blue 8-edges are considered distinct.

8-8 duopyramid

The dual of a 8-8 duoprism is called a 8-8 duopyramid. It has 64 tetragonal disphenoid cells, 128 triangular faces, 80 edges, and 16 vertices.

Related complex polygon

The regular complex polygon ₂{4}₈ has 16 vertices in C 2 with a real represention in R 4 matching the same vertex arrangement of the 8-8 duopyramid. It has 64 2-edges corresponding to the connecting edges of the 8-8 duopyramid, while the 16 edges connecting the two octagons are not included.

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