# 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[edit | edit source]

Consider the *n*/*d*-gonal *n*/*d*-gonal-antiprismatic duoprism, whose tera are *n* *n*/*d*-antiprismatic prisms, 2*n* 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 2*n n*/*d*-antiprismatic prisms and 4*n* triangular-*n*/*d* duoprisms.

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

The circumradius is .

## In higher dimensions[edit | edit source]

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.