Sphenocorona
In geometry, the sphenocorona is a Johnson solid with 12 equilateral triangles and 2 squares as its faces.
Properties
The sphenocorona 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 -corona refers to a crownlike complex of 8 equilateral triangles. By joining both complexes together, the resulting polyhedron has 12 equilateral triangles and 2 squares, making 14 faces. A convex polyhedron in which all faces are regular polygons is called a Johnson solid. The sphenocorona is among them, enumerated as the 86th Johnson solid. It is an elementary polyhedron, meaning it cannot be separated by a plane into two small regular-faced polyhedra.The surface area of a sphenocorona with edge length can be calculated as:
and its volume as:
Cartesian coordinates
Let be the smallest positive root of the quartic polynomial. Then, Cartesian [coordinate system|Cartesian coordinates] of a sphenocorona with edge length 2 are given by the union of the orbits of the pointsunder the action of the group generated by reflections about the xz-plane and the yz-plane.