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Edge-contracted icosahedron

Index Edge-contracted icosahedron

In geometry, an edge-contracted icosahedron is a polyhedron with 18 triangular faces, 27 edges, and 11 vertices with C2v symmetry, order 4. [1]

29 relations: Antiprism, Boron, Chemistry, Circumscribed sphere, Convex polytope, Cyclic group, Deltahedron, Edge contraction, Elongated octahedron, Equilateral triangle, Face (geometry), Geometry, Hexagon, Hydrogen, Icosahedron, John Horton Conway, Johnson solid, Net (polyhedron), Octadecahedron, Pentagon, Polyhedral skeletal electron pair theory, Polyhedron, Polyiamond, Polytope, Pyramid (geometry), Square, Triangle, Vertex configuration, Vertex figure.

Antiprism

In geometry, an n-sided antiprism is a polyhedron composed of two parallel copies of some particular n-sided polygon, connected by an alternating band of triangles.

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Boron

Boron is a chemical element with symbol B and atomic number 5.

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Chemistry

Chemistry is the scientific discipline involved with compounds composed of atoms, i.e. elements, and molecules, i.e. combinations of atoms: their composition, structure, properties, behavior and the changes they undergo during a reaction with other compounds.

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Circumscribed sphere

In geometry, a circumscribed sphere of a polyhedron is a sphere that contains the polyhedron and touches each of the polyhedron's vertices.

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Convex polytope

A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn.

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Cyclic group

In algebra, a cyclic group or monogenous group is a group that is generated by a single element.

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Deltahedron

In geometry, a deltahedron (plural deltahedra) is a polyhedron whose faces are all equilateral triangles.

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Edge contraction

In graph theory, an edge contraction is an operation which removes an edge from a graph while simultaneously merging the two vertices that it previously joined.

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Elongated octahedron

In geometry, an elongated octahedron is a polyhedron with 8 faces (4 triangular, 4 isosceles trapezoidal), 14 edges, and 8 vertices.

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Equilateral triangle

In geometry, an equilateral triangle is a triangle in which all three sides are equal.

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Face (geometry)

In solid geometry, a face is a flat (planar) surface that forms part of the boundary of a solid object; a three-dimensional solid bounded exclusively by flat faces is a polyhedron.

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Geometry

Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

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Hexagon

In geometry, a hexagon (from Greek ἕξ hex, "six" and γωνία, gonía, "corner, angle") is a six-sided polygon or 6-gon.

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Hydrogen

Hydrogen is a chemical element with symbol H and atomic number 1.

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Icosahedron

In geometry, an icosahedron is a polyhedron with 20 faces.

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John Horton Conway

John Horton Conway FRS (born 26 December 1937) is an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory.

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Johnson solid

In geometry, a Johnson solid is a strictly convex polyhedron, which is not uniform (i.e., not a Platonic solid, Archimedean solid, prism, or antiprism), and each face of which is a regular polygon.

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Net (polyhedron)

In geometry a net of a polyhedron is an arrangement of edge-joined polygons in the plane which can be folded (along edges) to become the faces of the polyhedron.

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Octadecahedron

In geometry, an octadecahedron (or octakaidecahedron) is a polyhedron with 18 faces.

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Pentagon

In geometry, a pentagon (from the Greek πέντε pente and γωνία gonia, meaning five and angle) is any five-sided polygon or 5-gon.

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Polyhedral skeletal electron pair theory

In chemistry the polyhedral skeletal electron pair theory (PSEPT) provides electron counting rules useful for predicting the structures of clusters such as borane and carborane clusters.

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Polyhedron

In geometry, a polyhedron (plural polyhedra or polyhedrons) is a solid in three dimensions with flat polygonal faces, straight edges and sharp corners or vertices.

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Polyiamond

A polyiamond (also polyamond or simply iamond) is a polyform whose base form is an equilateral triangle.

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Polytope

In elementary geometry, a polytope is a geometric object with "flat" sides.

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Pyramid (geometry)

In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex.

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Square

In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or (100-gradian angles or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted.

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Triangle

A triangle is a polygon with three edges and three vertices.

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Vertex configuration

In geometry, a vertex configuration by Walter Steurer, Sofia Deloudi, (2009) pp.

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Vertex figure

In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off.

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Redirects here:

Dissected icosahedron, Dissected regular icosahedron, Edge-diminished icosahedron.

References

[1] https://en.wikipedia.org/wiki/Edge-contracted_icosahedron

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