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89th Johnson solid (21 faces) From Wikipedia, the free encyclopedia
In geometry, the hebesphenomegacorona is a Johnson solid with 18 equilateral triangles and 3 squares as its faces.
Hebesphenomegacorona | |
---|---|
Type | Johnson J88 – J89 – J90 |
Faces | 3x2+3x4 triangles 1+2 squares |
Edges | 33 |
Vertices | 14 |
Vertex configuration | 4(32.42) 2+2x2(35) 4(34.4) |
Symmetry group | C2v |
Properties | convex, elementary |
Net | |
The hebesphenomegacorona is named by Johnson (1966) 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.[1] By joining both complexes together, the result polyhedron has 18 equilateral triangles and 3 squares, making 21 faces.[2]. 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 .[3] It is an elementary polyhedron, meaning it cannot be separated by a plane into two small regular-faced polyhedra.[4]
The surface area of a hebesphenomegacorona with edge length can be determined by adding the area of its faces, 18 equilateral triangles and 3 squares and its volume is .[2]
Let be the second smallest positive root of the polynomial Then, Cartesian coordinates of a hebesphenomegacorona 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.[5]
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