Polygonal duoprismatic spinoalterprism

A polygonal duoprismatic spinoalterprism is a uniform polyteron that consists of two pseudo-bases in like orientations connected by polygonal antiprismatic prisms and triangular-polygonal duoprisms.

Uniform duoprismatic spinoalterprisms exist for any regular polygon {n/d} where n/d > 1.5.

These make up one of four infinite families of uniform polytera, the others being the polygonal-uniform polyhedral duoprisms, the polygonal-polygonal antiprismatic duoprisms, and the polygonal-duoprismatic prisms.

Construction

Consider the n/d-gonal n/d-gonal-antiprismatic duoprism, whose tera are n n/d-antiprismatic prisms, 2n triangular-n/d duoprisms, and 2 n/d-n/d duoprisms. The duoprisms share half their cells with the antiprismatic prisms and the other half with the triangular-n/d duoprisms. This polyteron and a copy can blend on a common duoprism, such that every ridge now connects antiprismatic prisms to triangular-n/d duoprisms.

If d is even, only two blend components are required, producing a polyteron with 2n n/d-antiprismatic prisms and 4n triangular-n/d duoprisms.

If d is odd, four blend components are required. The resulting structure is more like the following: a hollowed compound of 2 bidual n/d-n/d duoprisms (like one would find in a duoantiprism's army) atop an alternate copy, with 4n n/d-antiprismatic prisms and 8n triangular-n/d duoprisms.

The circumradius is ${\displaystyle {\sqrt {{\frac {3+\cos {\frac {d\pi }{n}}}{8\sin ^{2}{\frac {d\pi }{n}}}}+{\frac {1}{4}}}}}$.

In higher dimensions

A similar construction involving polygonal-multiprismatic polygonal-antiprismatic duoprisms exists in all odd dimensions. This also works with higher-rank polytopes and their alterprisms. Whether either construction produces uniform polytopes from uniform bases is unknown.