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Regular icosahedron and Regular polyhedron

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

Difference between Regular icosahedron and Regular polyhedron

Regular icosahedron vs. Regular polyhedron

In geometry, a regular icosahedron is a convex polyhedron with 20 faces, 30 edges and 12 vertices. A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags.

Similarities between Regular icosahedron and Regular polyhedron

Regular icosahedron and Regular polyhedron have 31 things in common (in Unionpedia): Angular defect, Coxeter element, Digon, Dihedral angle, Dodecahedron, Dual polyhedron, Ernst Haeckel, Euclidean space, Facet (geometry), Faceting, Great dodecahedron, Great icosahedron, Hyperbolic space, Isogonal figure, Kepler–Poinsot polyhedron, Octahedron, Platonic solid, Polyhedron, Polytope, Radiolaria, Regular dodecahedron, Schläfli symbol, Small stellated dodecahedron, Sphere, Spherical polyhedron, Stellation, Stereographic projection, Symmetry group, Tetrahedron, Vertex figure, ..., Virus. Expand index (1 more) »

Angular defect

In geometry, the (angular) defect (or deficit or deficiency) means the failure of some angles to add up to the expected amount of 360° or 180°, when such angles in the Euclidean plane would.

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Coxeter element

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

Coxeter element and Regular icosahedron · Coxeter element and Regular polyhedron · See more »

Digon

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

Digon and Regular icosahedron · Digon and Regular polyhedron · See more »

Dihedral angle

A dihedral angle is the angle between two intersecting planes.

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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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Ernst Haeckel

Ernst Heinrich Philipp August Haeckel (16 February 1834 – 9 August 1919) was a German biologist, naturalist, philosopher, physician, professor, marine biologist, and artist who discovered, described and named thousands of new species, mapped a genealogical tree relating all life forms, and coined many terms in biology, including anthropogeny, ecology, phylum, phylogeny, and Protista. Haeckel promoted and popularised Charles Darwin's work in Germany and developed the influential but no longer widely held recapitulation theory ("ontogeny recapitulates phylogeny") claiming that an individual organism's biological development, or ontogeny, parallels and summarises its species' evolutionary development, or phylogeny.

Ernst Haeckel and Regular icosahedron · Ernst Haeckel and Regular polyhedron · See more »

Euclidean space

In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.

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Facet (geometry)

In geometry, a facet is a feature of a polyhedron, polytope, or related geometric structure, generally of dimension one less than the structure itself.

Facet (geometry) and Regular icosahedron · Facet (geometry) and Regular polyhedron · See more »

Faceting

Stella octangula as a faceting of the cube In geometry, faceting (also spelled facetting) is the process of removing parts of a polygon, polyhedron or polytope, without creating any new vertices.

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Great dodecahedron

In geometry, the great dodecahedron is a Kepler–Poinsot polyhedron, with Schläfli symbol and Coxeter–Dynkin diagram of.

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Great icosahedron

In geometry, the great icosahedron is one of four Kepler-Poinsot polyhedra (nonconvex regular polyhedra), with Schläfli symbol and Coxeter-Dynkin diagram of.

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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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Isogonal figure

In geometry, a polytope (a polygon, polyhedron or tiling, for example) is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure.

Isogonal figure and Regular icosahedron · Isogonal figure and Regular polyhedron · See more »

Kepler–Poinsot polyhedron

In geometry, a Kepler–Poinsot polyhedron is any of four regular star polyhedra.

Kepler–Poinsot polyhedron and Regular icosahedron · Kepler–Poinsot polyhedron and Regular polyhedron · See more »

Octahedron

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

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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

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

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Radiolaria

The Radiolaria, also called Radiozoa, are protozoa of diameter 0.1–0.2 mm that produce intricate mineral skeletons, typically with a central capsule dividing the cell into the inner and outer portions of endoplasm and ectoplasm.The elaborate mineral skeleton is usually made of silica.

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Regular dodecahedron

A regular dodecahedron or pentagonal dodecahedron is a dodecahedron that is regular, which is composed of twelve regular pentagonal faces, three meeting at each vertex.

Regular dodecahedron and Regular icosahedron · Regular dodecahedron and Regular polyhedron · See more »

Schläfli symbol

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

Regular icosahedron and Schläfli symbol · Regular polyhedron and Schläfli symbol · See more »

Small stellated dodecahedron

In geometry, the small stellated dodecahedron is a Kepler-Poinsot polyhedron, named by Arthur Cayley, and with Schläfli symbol.

Regular icosahedron and Small stellated dodecahedron · Regular polyhedron and Small stellated dodecahedron · See more »

Sphere

A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").

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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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Stellation

In geometry, stellation is the process of extending a polygon in two dimensions, polyhedron in three dimensions, or, in general, a polytope in n dimensions to form a new figure.

Regular icosahedron and Stellation · Regular polyhedron and Stellation · See more »

Stereographic projection

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

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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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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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Virus

A virus is a small infectious agent that replicates only inside the living cells of other organisms.

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The list above answers the following questions

Regular icosahedron and Regular polyhedron Comparison

Regular icosahedron has 163 relations, while Regular polyhedron has 138. As they have in common 31, the Jaccard index is 10.30% = 31 / (163 + 138).

References

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

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