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Regular icosahedron and Tetrahedron

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Regular icosahedron and Tetrahedron

Regular icosahedron vs. Tetrahedron

In geometry, a regular icosahedron is a convex polyhedron with 20 faces, 30 edges and 12 vertices. In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners.

Similarities between Regular icosahedron and Tetrahedron

Regular icosahedron and Tetrahedron have 41 things in common (in Unionpedia): Alternating group, American Mathematical Monthly, Antiprism, Conformal map, Coxeter element, Coxeter–Dynkin diagram, Digon, Dihedral angle, Distance-regular graph, Distance-transitive graph, Dodecahedron, Dual polyhedron, Face (geometry), Geometry, Graph (discrete mathematics), Hamiltonian path, Hyperbolic space, K-vertex-connected graph, List of finite spherical symmetry groups, N-skeleton, Net (polyhedron), Octahedron, Orbifold notation, Orthographic projection, Planar graph, Platonic graph, Platonic solid, Polyhedron, Polytope compound, Projection (linear algebra), ..., Regular graph, Schläfli symbol, Spherical polyhedron, Stereographic projection, Symmetric graph, Symmetric group, Symmetry group, Tangent, Tetrahedron, Vertex figure, Volume. Expand index (11 more) »

Alternating group

In mathematics, an alternating group is the group of even permutations of a finite set.

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American Mathematical Monthly

The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894.

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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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Conformal map

In mathematics, a conformal map is a function that preserves angles locally.

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Coxeter element

In mathematics, the Coxeter number h is the order of a Coxeter element of an irreducible Coxeter group.

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Coxeter–Dynkin diagram

In geometry, a Coxeter–Dynkin diagram (or Coxeter diagram, Coxeter graph) is a graph with numerically labeled edges (called branches) representing the spatial relations between a collection of mirrors (or reflecting hyperplanes).

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Digon

In geometry, a digon is a polygon with two sides (edges) and two vertices.

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Dihedral angle

A dihedral angle is the angle between two intersecting planes.

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Distance-regular graph

In mathematics, a distance-regular graph is a regular graph such that for any two vertices v and w, the number of vertices at distance j from v and at distance k from w depends only upon j, k, and i.

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Distance-transitive graph

In the mathematical field of graph theory, a distance-transitive graph is a graph such that, given any two vertices v and w at any distance i, and any other two vertices x and y at the same distance, there is an automorphism of the graph that carries v to x and w to y.

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Dodecahedron

In geometry, a dodecahedron (Greek δωδεκάεδρον, from δώδεκα dōdeka "twelve" + ἕδρα hédra "base", "seat" or "face") is any polyhedron with twelve flat faces.

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Dual polyhedron

In geometry, any polyhedron is associated with a second dual figure, where the vertices of one correspond to the faces of the other and the edges between pairs of vertices of one correspond to the edges between pairs of faces of the other.

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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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Graph (discrete mathematics)

In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".

Graph (discrete mathematics) and Regular icosahedron · Graph (discrete mathematics) and Tetrahedron · See more »

Hamiltonian path

In the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once.

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Hyperbolic space

In mathematics, hyperbolic space is a homogeneous space that has a constant negative curvature, where in this case the curvature is the sectional curvature.

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K-vertex-connected graph

In graph theory, a connected graph G is said to be k-vertex-connected (or k-connected) if it has more than k vertices and remains connected whenever fewer than k vertices are removed.

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List of finite spherical symmetry groups

Finite spherical symmetry groups are also called point groups in three dimensions.

List of finite spherical symmetry groups and Regular icosahedron · List of finite spherical symmetry groups and Tetrahedron · See more »

N-skeleton

In mathematics, particularly in algebraic topology, the of a topological space X presented as a simplicial complex (resp. CW complex) refers to the subspace Xn that is the union of the simplices of X (resp. cells of X) of dimensions In other words, given an inductive definition of a complex, the is obtained by stopping at the.

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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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Octahedron

In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces, twelve edges, and six vertices.

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Orbifold notation

In geometry, orbifold notation (or orbifold signature) is a system, invented by William Thurston and popularized by the mathematician John Conway, for representing types of symmetry groups in two-dimensional spaces of constant curvature.

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Orthographic projection

Orthographic projection (sometimes orthogonal projection), is a means of representing three-dimensional objects in two dimensions.

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Planar graph

In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints.

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Platonic graph

In the mathematical field of graph theory, a Platonic graph is a graph that has one of the Platonic solids as its skeleton.

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Platonic solid

In three-dimensional space, a Platonic solid is a regular, convex polyhedron.

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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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Polytope compound

A polyhedral compound is a figure that is composed of several polyhedra sharing a common centre.

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Projection (linear algebra)

In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that.

Projection (linear algebra) and Regular icosahedron · Projection (linear algebra) and Tetrahedron · See more »

Regular graph

In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency.

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Schläfli symbol

In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.

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Spherical polyhedron

In mathematics, a spherical polyhedron or spherical tiling is a tiling of the sphere in which the surface is divided or partitioned by great arcs into bounded regions called spherical polygons.

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Stereographic projection

In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane.

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Symmetric graph

In the mathematical field of graph theory, a graph G is symmetric (or arc-transitive) if, given any two pairs of adjacent vertices u1—v1 and u2—v2 of G, there is an automorphism such that In other words, a graph is symmetric if its automorphism group acts transitively upon ordered pairs of adjacent vertices (that is, upon edges considered as having a direction).

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Symmetric group

In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions.

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Symmetry group

In group theory, the symmetry group of an object (image, signal, etc.) is the group of all transformations under which the object is invariant with composition as the group operation.

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Tangent

In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point.

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Tetrahedron

In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners.

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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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Volume

Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains.

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The list above answers the following questions

Regular icosahedron and Tetrahedron Comparison

Regular icosahedron has 163 relations, while Tetrahedron has 202. As they have in common 41, the Jaccard index is 11.23% = 41 / (163 + 202).

References

This article shows the relationship between Regular icosahedron and Tetrahedron. To access each article from which the information was extracted, please visit:

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