Square antiprism has part(s) of the class vertex
Crossed antiprism
A crossed square antiprism is a star polyhedron, topologically identical to the square antiprism with the same vertex arrangement, but it can't be made uniform; the sides are isosceles triangles. Its vertex configuration is 3.3/2.3.4, with one triangle retrograde.  It has d4d symmetry, order 8.Symmetry mutation
As an antiprism, the square antiprism belongs to a family of polyhedra that includes the octahedron (which can be seen as a triangle-capped antiprism), the pentagonal antiprism, the hexagonal antiprism, and the octagonal antiprism.The square antiprism is first in a series of snub polyhedra and tilings with vertex figure 3.3.4.3.n.
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