Related Polyhedra
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 gyroelongated square pyramid is a Johnson solid (specifically, J10) constructed by replacing one square of a square antiprism with a square pyramid. Similarly, the gyroelongated square bipyramid (J17) is a deltahedron (a polyhedron whose faces are all equilateral triangles) constructed by replacing both squares of a square antiprism with a square pyramid.
The snub disphenoid (J84) is another deltahedron, constructed by replacing the two squares of a square antiprism by pairs of equilateral triangles. The snub square antiprism (J85) can be seen as a square antiprism with a chain of equilateral triangles inserted around the middle. The sphenocorona (J86) and the sphenomegacorona (J88) are other Johnson solids that, like the square antiprism, consist of two squares and an even number of equilateral triangles.
The square antiprism is first in a series of snub polyhedra and tilings with vertex figure 3.3.4.3.n.
| Symmetry 4n2 + |
Spherical | Euclidean | Hyperbolic | |||||
|---|---|---|---|---|---|---|---|---|
| 242 + |
342 + |
442 + |
542 + |
642 + |
742 + |
842 + |
∞42 + |
|
| Snub figure |
3.3.4.3.2 |
3.3.4.3.3 |
3.3.4.3.4 |
3.3.4.3.5 |
3.3.4.3.6 |
3.3.4.3.7 |
3.3.4.3.8 |
3.3.4.3.∞ |
| Coxeter Schläfli |
s{2,4} |
s{3,4} |
s{4,4} |
s{5,4} |
s{6,4} |
s{7,4} |
s{8,4} |
s{∞,4} |
| Snub dual figure |
V3.3.4.3.2 |
V3.3.4.3.3 |
V3.3.4.3.4 |
V3.3.4.3.5 |
V3.3.4.3.6 | V3.3.4.3.7 | V3.3.4.3.8 | V3.3.4.3.∞ |
| Coxeter | ||||||||
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