Hebesphenomegacorona Explained

Type:	Johnson
Faces:	3x2+3x4 triangles 1+2 squares
Edges:	33
Vertices:	14
Net:	Johnson solid 89 net.png

In geometry, the hebesphenomegacorona is a Johnson solid with 18 equilateral triangles and 3 squares as its faces.

Properties

The hebesphenomegacorona is named by in which he used the prefix hebespheno- referring to a blunt wedge-like complex formed by three adjacent lunes - a square with equilateral triangles attached on its opposite sides. The suffix -megacorona refers to a crownlike complex of 12 triangles. By joining both complexes together, the result polyhedron has 18 equilateral triangles and 3 squares, making 21 faces.. All of its faces are regular polygons, categorizing the hebesphenomegacorona as a Johnson solid - a convex polyhedron in which all of its faces are regular polygons - enumerated as 89th Johnson solid

J _{89} . It is elementary, meaning it cannot be separated by a plane into two small regular-faced polyhedra.

The surface area of a hebesphenomegacorona with edge length

a can be determined by adding the area of its faces, 18 equilateral triangles and 3 squares$$\backslash fraca^2\; \backslash approx\; 10.7942a^2,$$and its volume is 2 . 9129 a ^{3} .

Cartesian coordinates

Let

a ≈ 0 . 21684 be the second smallest positive root of the polynomialThen, Cartesian coordinates of a hebesphenomegacorona 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