Duotruncatoalterprism

A duotruncatoalterprism is an isogonal polytope formed from the convex hull of two orthogonal duoprisms where one base is a truncated version of the other, in such a way that a ring of alternating polygons is formed. They are closely related to the duoexpandoprisms and duotruncatoprisms, and are somewhere in between these two families. The simplest possible duotruncatoalterprism is the digonal-square prismantiprismoid, which can be thought of as a digonal duotruncatoalterprism, while the simplest unique duoexpandoprism is the triangular duotruncatoalterprism, which is the convex hull of two orthogonal triangular-ditrigonal duoprisms. The dual of a duotruncatoalterprism is a duotruncatoaltertegum.

Unlike the duoexpandoprisms, which have the expanded hypercube as its only uniform solution, there are no uniform duotruncatoalterprisms, and they cannot be optimized either with the exception of the digonal-square prismantiprismoid, because it necessarily has a variant that approaches the minimal value but never reaches it within its topology.

The 4D duotruncatoalterprisms have one ring of 2n n-gonal prisms and a second ring of 4n n-gonal cupolas in alternating orientations, connected by a layer of tetragonal disphenoids and rectangular trapezoprisms. Their vertex figures are variations of a polyhedron formed by augmenting a pyramid onto one of the isosceles triangles of an isosceles trapezoidal pyramid. 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.