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Platonic solid and Regular icosahedron

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

Difference between Platonic solid and Regular icosahedron

Platonic solid vs. Regular icosahedron

In three-dimensional space, a Platonic solid is a regular, convex polyhedron. In geometry, a regular icosahedron is a convex polyhedron with 20 faces, 30 edges and 12 vertices.

Similarities between Platonic solid and Regular icosahedron

Platonic solid and Regular icosahedron have 39 things in common (in Unionpedia): Angular defect, Antiprism, Compound of two icosahedra, Coxeter element, Dihedral angle, Dodecahedron, Dual polyhedron, Ernst Haeckel, Euclidean space, Face (geometry), Genome, Geodesic grid, Golden ratio, Icosahedral symmetry, Icosahedron, Isogonal figure, Johnson solid, Kepler–Poinsot polyhedron, Octahedron, Orbifold notation, Polyhedron, Polytope, Polytope compound, Protein, Radiolaria, Radius, Regular 4-polytope, Regular dodecahedron, Regular polyhedron, Role-playing game, ..., Schläfli symbol, Sphere, Stellation, Symmetry group, Tetrahedral symmetry, Tetrahedron, Vertex figure, Virus, Volume. Expand index (9 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.

Angular defect and Platonic solid · Angular defect and Regular icosahedron · See more »

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.

Antiprism and Platonic solid · Antiprism and Regular icosahedron · See more »

Compound of two icosahedra

This uniform polyhedron compound is a composition of 2 icosahedra.

Compound of two icosahedra and Platonic solid · Compound of two icosahedra and Regular icosahedron · See more »

Coxeter element

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

Coxeter element and Platonic solid · Coxeter element and Regular icosahedron · See more »

Dihedral angle

A dihedral angle is the angle between two intersecting planes.

Dihedral angle and Platonic solid · Dihedral angle and Regular icosahedron · See more »

Dodecahedron

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

Dodecahedron and Platonic solid · Dodecahedron and Regular icosahedron · See more »

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.

Dual polyhedron and Platonic solid · Dual polyhedron and Regular icosahedron · See more »

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 Platonic solid · Ernst Haeckel and Regular icosahedron · 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.

Euclidean space and Platonic solid · Euclidean space and Regular icosahedron · See more »

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.

Face (geometry) and Platonic solid · Face (geometry) and Regular icosahedron · See more »

Genome

In the fields of molecular biology and genetics, a genome is the genetic material of an organism.

Genome and Platonic solid · Genome and Regular icosahedron · See more »

Geodesic grid

A geodesic grid is a spatial grid based on a geodesic polyhedron or Goldberg polyhedron.

Geodesic grid and Platonic solid · Geodesic grid and Regular icosahedron · See more »

Golden ratio

In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.

Golden ratio and Platonic solid · Golden ratio and Regular icosahedron · See more »

Icosahedral symmetry

A regular icosahedron has 60 rotational (or orientation-preserving) symmetries, and a symmetry order of 120 including transformations that combine a reflection and a rotation.

Icosahedral symmetry and Platonic solid · Icosahedral symmetry and Regular icosahedron · See more »

Icosahedron

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

Icosahedron and Platonic solid · Icosahedron and Regular icosahedron · See more »

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 Platonic solid · Isogonal figure and Regular icosahedron · See more »

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.

Johnson solid and Platonic solid · Johnson solid and Regular icosahedron · See more »

Kepler–Poinsot polyhedron

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

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

Octahedron

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

Octahedron and Platonic solid · Octahedron and Regular icosahedron · See more »

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.

Orbifold notation and Platonic solid · Orbifold notation and Regular icosahedron · See more »

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.

Platonic solid and Polyhedron · Polyhedron and Regular icosahedron · See more »

Polytope

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

Platonic solid and Polytope · Polytope and Regular icosahedron · See more »

Polytope compound

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

Platonic solid and Polytope compound · Polytope compound and Regular icosahedron · See more »

Protein

Proteins are large biomolecules, or macromolecules, consisting of one or more long chains of amino acid residues.

Platonic solid and Protein · Protein and Regular icosahedron · See more »

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.

Platonic solid and Radiolaria · Radiolaria and Regular icosahedron · See more »

Radius

In classical geometry, a radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length.

Platonic solid and Radius · Radius and Regular icosahedron · See more »

Regular 4-polytope

In mathematics, a regular 4-polytope is a regular four-dimensional polytope.

Platonic solid and Regular 4-polytope · Regular 4-polytope and Regular icosahedron · See more »

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.

Platonic solid and Regular dodecahedron · Regular dodecahedron and Regular icosahedron · See more »

Regular polyhedron

A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags.

Platonic solid and Regular polyhedron · Regular icosahedron and Regular polyhedron · See more »

Role-playing game

A role-playing game (sometimes spelled roleplaying game and abbreviated to RPG) is a game in which players assume the roles of characters in a fictional setting.

Platonic solid and Role-playing game · Regular icosahedron and Role-playing game · See more »

Schläfli symbol

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

Platonic solid and Schläfli symbol · Regular icosahedron and Schläfli symbol · 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").

Platonic solid and Sphere · Regular icosahedron and Sphere · See more »

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.

Platonic solid and Stellation · Regular icosahedron and Stellation · See more »

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.

Platonic solid and Symmetry group · Regular icosahedron and Symmetry group · See more »

Tetrahedral symmetry

A regular tetrahedron, an example of a solid with full tetrahedral symmetry A regular tetrahedron has 12 rotational (or orientation-preserving) symmetries, and a symmetry order of 24 including transformations that combine a reflection and a rotation.

Platonic solid and Tetrahedral symmetry · Regular icosahedron and Tetrahedral symmetry · See more »

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.

Platonic solid and Tetrahedron · Regular icosahedron and Tetrahedron · See more »

Vertex figure

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

Platonic solid and Vertex figure · Regular icosahedron and Vertex figure · See more »

Virus

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

Platonic solid and Virus · Regular icosahedron and Virus · See more »

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.

Platonic solid and Volume · Regular icosahedron and Volume · See more »

The list above answers the following questions

Platonic solid and Regular icosahedron Comparison

Platonic solid has 190 relations, while Regular icosahedron has 163. As they have in common 39, the Jaccard index is 11.05% = 39 / (190 + 163).

References

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

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