Snub square antiprism
Encyclopedia
In geometry
, the snub square antiprism is one of the
Johnson solid
s (J85).
It is one of the elementary Johnson solids that do not arise from "cut and paste" manipulations of the Platonic
and Archimedean
solids, although it is a relative of the Icosahedron
that has fourfold symmetry instead of threefold.
The 92 Johnson solids were named and described by Norman Johnson in 1966.
It can be thought of as a square antiprism
with a chain of triangles inserted around the middle. A similar effect can be achieved with a triangular antiprism (which is an octahedron
), resulting in an icosahedron
.
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, the snub square antiprism is one of the
Johnson solid
Johnson solid
In geometry, a Johnson solid is a strictly convex polyhedron, each face of which is a regular polygon, but which is not uniform, i.e., not a Platonic solid, Archimedean solid, prism or antiprism. There is no requirement that each face must be the same polygon, or that the same polygons join around...
s (J85).
It is one of the elementary Johnson solids that do not arise from "cut and paste" manipulations of the Platonic
Platonic solid
In geometry, a Platonic solid is a convex polyhedron that is regular, in the sense of a regular polygon. Specifically, the faces of a Platonic solid are congruent regular polygons, with the same number of faces meeting at each vertex; thus, all its edges are congruent, as are its vertices and...
and Archimedean
Archimedean solid
In geometry an Archimedean solid is a highly symmetric, semi-regular convex polyhedron composed of two or more types of regular polygons meeting in identical vertices...
solids, although it is a relative of the Icosahedron
Icosahedron
In geometry, an icosahedron is a regular polyhedron with 20 identical equilateral triangular faces, 30 edges and 12 vertices. It is one of the five Platonic solids....
that has fourfold symmetry instead of threefold.
The 92 Johnson solids were named and described by Norman Johnson in 1966.
It can be thought of as a square antiprism
Square antiprism
In geometry, the square antiprism is the second in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps...
with a chain of triangles inserted around the middle. A similar effect can be achieved with a triangular antiprism (which is an octahedron
Octahedron
In geometry, an octahedron is a polyhedron with eight faces. A regular octahedron is a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex....
), resulting in an icosahedron
Icosahedron
In geometry, an icosahedron is a regular polyhedron with 20 identical equilateral triangular faces, 30 edges and 12 vertices. It is one of the five Platonic solids....
.