Английская Википедия:Edge-contracted icosahedron

Материал из Онлайн справочника
Перейти к навигацииПерейти к поиску

Шаблон:Short description Шаблон:Infobox polyhedron

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 (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[1]), it has 10 vertices, 22 edges, and 14 faces, 12 triangles Файл:Polyiamond-1-1.svg and 2 triamonds Файл:Polyiamond-3-1.svg.

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.

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.[2]

Файл:Dissected regular icosahedron.png

In chemistry

In chemistry, this polyhedron is most commonly called the octadecahedron, for 18 triangular faces, and represents the closo-boranate Шаблон:Chem2. [3]

Файл:Closo-undecaborate(11)-dianion-from-xtal-3D-bs-17.png
Ball-and-stick model of the
closo-undecaborate ion, Шаблон:Chem2
Файл:Octadecahedron B11H11 2− structure.gif
closo-boranate Шаблон:Chem2
Файл:Net of octadecahedron B11H11 2− structure.svg
Net

Related polyhedra

The elongated octahedron is similar to the edge-contracted icosahedron, but instead of only one edge contracted, two opposite edges are contracted.

References

Шаблон:Reflist

External links

Шаблон:Polyhedra

  1. Шаблон:Cite web
  2. John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, Шаблон:ISBN (Chapter 26) The Grand Antiprism
  3. Шаблон:Holleman&Wiberg