User:Tomruen/10-10 duoprism

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

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.

Related complex polygons
The regular complex polytope 10{4}2,, in $$\mathbb{C}^2$$ 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 or decagonal duopyramid. It has 100 tetragonal disphenoid cells, 200 triangular faces, 120 edges, and 20 vertices.

Orthogonal projection

Related complex polygon


The regular complex polygon 2{4}10 has 20 vertices in $$\mathbb{C}^2$$ with a real representation in $$\mathbb{R}^4$$ 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.

Related polytopes
The 5-5 duoantiprism is an alternation of the 10-10 duoprism, but is not uniform. It has a highest symmetry construction of order 400 uniquely obtained as a direct alternation of the uniform 10-10 duoprism with an edge length ratio of 0.743 : 1. It has 70 cells composed of 20 pentagonal antiprisms and 50 tetrahedra (as tetragonal disphenoids).

Vertex figure for the 5-5 duoantiprism