# CRFP4DP/Infinite families (Meta, 14)

### From Hi.gher. Space

The obvious infinite family is that of the *m*,*n*-duoprisms (*m* ≥ *n* ≥ 3).

There is also an infinite family of prisms of the *n*-gonal antiprisms.

Mrrl discovered an infinite family of ringed forms, with a 3-membered ring consisting of two antiprisms and a prism, with various Johnson polyhedra filling in the gaps. The first member contains two square antiprisms, one cube, four tetrahedra and four square pyramids. Details can be found in this post. In general, members of this family consists of two *n*-gonal antiprisms and an *n*-gonal prism, forming a 3-membered ring, with *n* tetrahedra and *n* square pyramids filling in the lateral gaps, for all *n* ≥ 3. Keiji has devised a similar naming scheme to the one he used for the cupolic rings: the collective term is the family of *biantiprismatic rings*, and the specific term is the *n*-gonal biantiprismatic ring, e.g. *square biantiprismatic ring*. These ringed forms are included as an infinite subfamily in Klitzing's list of segmentotopes where they are numbered among the *wedges*.

The n-gonal pyramid antiprisms (n-gonal pyramid || inverted gyro n-gonal pyramid) are CRF, and for n=4 and n=5, non-orbiform. (For n=3, it is identical to the 16-cell.) They are identical to the n-antiprism bipyramid.