Sphenomegacorona Explained

Type:	Johnson
Faces:	16 triangles 2 squares
Edges:	28
Vertices:	12
Dual:	-
Properties:	convex
Net:	Johnson solid 88 net.png

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 elementary, 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

k ≈ 0 . 59463 be the smallest positive root of the polynomial$$1680\; x^-\; 4800\; x^\; -\; 3712\; x^\; +\; 17216\; x^+\; 1568\; x^\; -\; 24576\; x^\; +\; 2464\; x^\; +\; 17248\; x^9\; -3384\; x^8\; -\; 5584\; x^7\; +\; 2000\; x^6+\; 240\; x^5-\; 776\; x^4+\; 304\; x^3\; +\; 200\; x^2\; -\; 56\; x\; -23.$$Then, Cartesian coordinates of a sphenomegacorona 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