Alterprism

An alterprism is a polytope constructed by lacing two geometrically-identical polytopes either in some gyrated orientations together, such as the truncated tetrahedral alterprism, or in the same orientation with intersecting laced facets, such as the small icosicosidodecahedral alterprism. Alternated prisms are a subset of alterprisms that can be formed from alternation of a prism.

Examples include laces of polytopes with simplicial or demicubic symmetry in any dimension, laces with icositetrachoric symmetry, or laces with the symmetry of the E6 family. Many of these polytopes are scaliform. A simple 4D example of this would be the truncated tetrahedral cupoliprism.

The only uniform 4D cases are the prismatic prisms, antiprismatic prisms, the hexadecachoron xo3oo3ox&#x, the tesseractihemioctachoron, the small ditrigonary icosidodecahedral antiprism xo5/2ox3oo3*a&#x, the great ditrigonary icosidodecahedral antiprism xo5ox3/2oo3*a&#x, and the blend of the latter two, the ditrigonary dodecadodecahedral antiprism. The latter three are called the Johnson antiprisms. In the fifth dimension, the uniform alterprisms are the triacontaditeron, the demipenteract, the dodecateron, the small ditetrahedronary hexacosihecatonicosachoric antiprism and the grand ditetrahedronary hexacosihecatonicosachoric antiprism and some of their facetings.