In geometry

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 augmented sphenocorona 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 (J₈₇), and is obtained by adding
a square pyramid

Square pyramid

In geometry, a square pyramid is a pyramid having a square base. If the apex is perpendicularly above the center of the square, it will have C4v symmetry.- Johnson solid :...

 to one of the square faces of the sphenocorona

Sphenocorona

In geometry, the sphenocorona is one of theJohnson solids .It is one of the elementary Johnson solids that do not arise from "cut and paste" manipulations of the Platonic and Archimedean solids....

.
It is the only Johnson solid arising from "cut and paste" manipulations where the components are not all sections of 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.

The 92 Johnson solids were named and described by Norman Johnson in 1966.

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