Truncatoprismantiprismoid

A truncatoprismantiprismoid is an isogonal polytope with a structure composed of two orthogonal rings of alternating prisms and trapezoprisms and are generally nonuniform. The simplest non-trivial prismantiprismoid is the digonal-triangular truncatoprismantiprismoid, because the digonal truncatoprismantiprismoid is none other than the square ditetragoltriate. The dual of a truncatoprismantiprismoid is an apiculatotegmantitegmoid. Additional cells of a truncatoprismantiprismoid include rectangular frustums (if the two bases are identical, then they become rectangular trapezoprisms). They are also a special class of the duoprismatic truncatoprismantiprismatoswirlprisms, having only two polygonal rotations for each ring.

Unlike the prismantiprismoids, the n-m truncatoprismantiprismoid is equivalent to the m-n truncatoprismantiprismoid, and can have double symmetry if n and m are identical. Like the prismantiprismoids, a restriction is that n and m must be an alternable polytope (such as a hexagonal prism).

Special cases

In four dimensions, an n-gonal truncatoprismantiprismoid can have the least possible edge length difference, assuming that the short edge length is 1, if the polygonal inradius of the short edge is equal to (1+√2cos(π/2n))/(2√2sin(π/2n)). This ensures that the isosceles trapezoids have three equal edges.