Edge-contracted icosahedron#Related polytopes

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 (each forming a half-hexagon), and thus is not a Johnson solid.

If the sets of three coplanar triangles are considered a single face (called a triamond{{Cite web|url=http://www.interocitors.com/polyhedra/Triamonds/|title=Convex Triamond Regular Polyhedra}}), 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 (an antiprismatic core with one square base and one pentagonal base); each base is then augmented with a pyramid.

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.John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, {{ISBN|978-1-56881-220-5}} (Chapter 26) The Grand Antiprism

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In chemistry, this polyhedron is most commonly called the octadecahedron, for 18 triangular faces, and represents the closo-boranate {{chem2|[B11H11](2-)}}. {{Holleman&Wiberg|page=1165}}

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• [http://www.interocitors.com/polyhedra/Deltahedra/Convex The Convex Deltahedra, And the Allowance of Coplanar Faces]

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Category:Deltahedra