A duoexpandoprism is an isogonal polytope formed from the convex hull of two orthogonal duoprisms where one base is an expanded version of the other, forming two orthogonal rings of 2n n-gonal prisms (with alternating heights). They are closely related to the duotruncatoprisms, differing only in the prisms and the number of rings. The simplest possible duoexpandoprism is the digonal-square prismantiprismoid, which can be thought of as a digonal duoexpandoprism, while the simplest unique duoexpandoprism is the triangular duoexpandoprism, which is the convex hull of two orthogonal triangular-ditrigonal duoprisms. The dual of a duoexpandoprism is a duoexpandotegum.
In four dimensions, the related n-gonal double truncatoprismantiprismoid is topologically identical to the 2n-gonal duoexpandoprism, but with only half the symmetry. This variant alternates prisms and trapezoprisms.
The 4D duoexpandoprisms have 2 rings of 2n n-gonal prisms, with the space between filled by a layer of rectangular trapezoprisms, tetragonal disphenoids, and wedges. The vertex figure is a highly distorted variant of the octahedron with only mirror symmetry. If n is equal to 2, then the prisms become rectangles and the vertex figure becomes a mirror-symmetric notch. Analogs in higher dimensions also exist.
Duoexpandoprisms can be blended with the base duoprisms to produce analogs of the four-dimensional inverted quasiprismatodishexadecachoron.
Special cases[edit | edit source]
In four dimensions, an n-gonal duoexpandoprism can have the least possible edge length difference, assuming that the prism heights are identical and the n-gon length is 1, if the n-gonal prism height is equal to (1+tan(π/2n)√)/4. This ensures that the lateral edges have length 1.
[edit | edit source]
- Klitzing, Richard. "n-dep".