Sphenomegacorona | |
---|---|
Type |
Johnson J87 – J88 – J89 |
Faces | 16
triangles 2 squares |
Edges | 28 |
Vertices | 12 |
Vertex configuration | 2(34) 2(32.42) 2x2(35) 4(34.4) |
Symmetry group | C2v |
Dual polyhedron | - |
Properties | convex |
Net | |
In geometry, the sphenomegacorona is a Johnson solid with 16 equilateral triangles and 2 squares as its faces.
The sphenomegacorona was named by Johnson (1966) 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. [1] By joining both complexes, the resulting polyhedron has 16 equilateral triangles and 2 squares, making 18 faces. [2] 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 . [3] It is elementary, meaning it cannot be separated by a plane into two small regular-faced polyhedra. [4]
The surface area of a sphenomegacorona 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 —is given by A334114. With edge length , its surface area and volume can be formulated as: [2] [5]
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. [6]
Sphenomegacorona | |
---|---|
Type |
Johnson J87 – J88 – J89 |
Faces | 16
triangles 2 squares |
Edges | 28 |
Vertices | 12 |
Vertex configuration | 2(34) 2(32.42) 2x2(35) 4(34.4) |
Symmetry group | C2v |
Dual polyhedron | - |
Properties | convex |
Net | |
In geometry, the sphenomegacorona is a Johnson solid with 16 equilateral triangles and 2 squares as its faces.
The sphenomegacorona was named by Johnson (1966) 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. [1] By joining both complexes, the resulting polyhedron has 16 equilateral triangles and 2 squares, making 18 faces. [2] 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 . [3] It is elementary, meaning it cannot be separated by a plane into two small regular-faced polyhedra. [4]
The surface area of a sphenomegacorona 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 —is given by A334114. With edge length , its surface area and volume can be formulated as: [2] [5]
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. [6]