In geometry, the sphenomegacorona is a Johnson solid with 16 equilateral triangles and 2 squares as its faces.

Properties

The sphenomegacorona was named by in which he used the prefix spheno- referring to a wedge-like complex formed by two adjacent lunes—a square with equilateral triangles attached on its opposite sides. The suffix -megacorona refers to a crownlike complex of 12 triangles, contrasted with the smaller triangular complex that makes the sphenocorona. By joining both complexes, the resulting polyhedron has 16 equilateral triangles and 2 squares, making 18 faces. All of its faces are regular polygons, categorizing the sphenomegacorona as a Johnson solid—a convex polyhedron in which all of the faces are regular polygons—enumerated as the 88th Johnson solid J_{88}. It is an elementary polyhedron, meaning it cannot be separated by a plane into two small regular-faced polyhedra. The surface area of a sphenomegacorona A is the total of polygonal faces' area—16 equilateral triangles and 2 squares. The volume of a sphenomegacorona is obtained by finding the root of a polynomial, and its decimal expansion—denoted as \xi—is given by. With edge length a, its surface area and volume can be formulated as:

Cartesian coordinates

Let be the smallest positive root of the polynomial Then, Cartesian coordinates of a sphenomegacorona with edge length 2 are given by the union of the orbits of the points under the action of the group generated by reflections about the xz-plane and the yz-plane.