Edge-contracted icosahedron
In geometry, an edge-contracted icosahedron is a polyhedron with 18 triangular faces, 27 edges, and 11 vertices.
Construction
It can be constructed from the regular icosahedron, with one edge contraction, removing one vertex, 3 edges, and 2 faces. This contraction distorts the circumscribed sphere original vertices. With all equilateral triangle faces, it has 2 sets of 3 coplanar equilateral triangles, and thus is not a Johnson solid.If the sets of three coplanar triangles are considered a single face, it has 10 vertices, 22 edges, and 14 faces, 12 triangles and 2 triamonds.
It may also be described as having a hybrid square-pentagonal antiprismatic core ; each base is then augmented with a pyramid.
Related polytopes
The dissected regular icosahedron is a variant topologically equivalent to the sphenocorona with the two sets of 3 coplanar faces as trapezoids. This is the vertex figure of a 4D polytope, grand antiprism. It has 10 vertices, 22 edges, and 12 equilateral triangular faces and 2 trapezoid faces.In chemistry
In chemistry, this polyhedron is most commonly called the octadecahedron, for 18 triangular faces, and represents the closo-boranate.Ball-and-stick model of the closo-undecaborate ion, | closo-boranate | Net |