# 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, eight blend components are required. The resulting polyteron is more like a 2n/2d-gonal example, with 8n n/d-antiprismatic prisms (as 2n 2n/2d-antiprismatic prisms) as and 8n triangular-n/d duoprisms (as 4n triangular-2n/2d duoprisms).

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

## 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.