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Polyhedron and Tetrahedron

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

Difference between Polyhedron and Tetrahedron

Polyhedron vs. Tetrahedron

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. 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 Polyhedron and Tetrahedron

Polyhedron and Tetrahedron have 40 things in common (in Unionpedia): American Mathematical Monthly, Antiprism, Complete graph, Convex polytope, Crystal, Cube, Digon, Dihedral angle, Dodecahedron, Dot product, Dual polyhedron, Edge (geometry), Face (geometry), Geometry, Graph (discrete mathematics), Graph theory, Harold Scott MacDonald Coxeter, Honeycomb (geometry), K-vertex-connected graph, N-skeleton, Net (polyhedron), Octahedron, Parallelepiped, Piero della Francesca, Planar graph, Platonic solid, Point groups in three dimensions, Polygon, Pyramid (geometry), Right angle, ..., Simplex, Symmetric graph, Symmetry group, Tetrahedron, Three-dimensional space, Trapezohedron, Uniform polyhedron, Vertex (geometry), Vertex figure, Volume. Expand index (10 more) »

American Mathematical Monthly

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

American Mathematical Monthly and Polyhedron · American Mathematical Monthly and Tetrahedron · 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 Polyhedron · Antiprism and Tetrahedron · See more »

Complete graph

No description.

Complete graph and Polyhedron · Complete graph and Tetrahedron · See more »

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.

Convex polytope and Polyhedron · Convex polytope and Tetrahedron · See more »

Crystal

A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions.

Crystal and Polyhedron · Crystal and Tetrahedron · See more »

Cube

In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.

Cube and Polyhedron · Cube and Tetrahedron · See more »

Digon

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

Digon and Polyhedron · Digon and Tetrahedron · See more »

Dihedral angle

A dihedral angle is the angle between two intersecting planes.

Dihedral angle and Polyhedron · Dihedral angle and Tetrahedron · 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 Polyhedron · Dodecahedron and Tetrahedron · See more »

Dot product

In mathematics, the dot product or scalar productThe term scalar product is often also used more generally to mean a symmetric bilinear form, for example for a pseudo-Euclidean space.

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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.

Dual polyhedron and Polyhedron · Dual polyhedron and Tetrahedron · See more »

Edge (geometry)

In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope.

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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.

Face (geometry) and Polyhedron · Face (geometry) and Tetrahedron · See more »

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.

Geometry and Polyhedron · Geometry and Tetrahedron · See more »

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 Polyhedron · Graph (discrete mathematics) and Tetrahedron · See more »

Graph theory

In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.

Graph theory and Polyhedron · Graph theory and Tetrahedron · See more »

Harold Scott MacDonald Coxeter

Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 – March 31, 2003) was a British-born Canadian geometer.

Harold Scott MacDonald Coxeter and Polyhedron · Harold Scott MacDonald Coxeter and Tetrahedron · See more »

Honeycomb (geometry)

In geometry, a honeycomb is a space filling or close packing of polyhedral or higher-dimensional cells, so that there are no gaps.

Honeycomb (geometry) and Polyhedron · Honeycomb (geometry) and Tetrahedron · See more »

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.

K-vertex-connected graph and Polyhedron · K-vertex-connected graph 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.

N-skeleton and Polyhedron · N-skeleton and Tetrahedron · See more »

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.

Net (polyhedron) and Polyhedron · Net (polyhedron) and Tetrahedron · See more »

Octahedron

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

Octahedron and Polyhedron · Octahedron and Tetrahedron · See more »

Parallelepiped

In geometry, a parallelepiped is a three-dimensional figure formed by six parallelograms (the term rhomboid is also sometimes used with this meaning).

Parallelepiped and Polyhedron · Parallelepiped and Tetrahedron · See more »

Piero della Francesca

Piero della Francesca (c. 1415 – 12 October 1492) was an Italian painter of the Early Renaissance.

Piero della Francesca and Polyhedron · Piero della Francesca and Tetrahedron · See more »

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.

Planar graph and Polyhedron · Planar graph and Tetrahedron · See more »

Platonic solid

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

Platonic solid and Polyhedron · Platonic solid and Tetrahedron · See more »

Point groups in three dimensions

In geometry, a point group in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry group of a sphere.

Point groups in three dimensions and Polyhedron · Point groups in three dimensions and Tetrahedron · See more »

Polygon

In elementary geometry, a polygon is a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed polygonal chain or circuit.

Polygon and Polyhedron · Polygon and Tetrahedron · See more »

Pyramid (geometry)

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

Polyhedron and Pyramid (geometry) · Pyramid (geometry) and Tetrahedron · See more »

Right angle

In geometry and trigonometry, a right angle is an angle of exactly 90° (degrees), corresponding to a quarter turn.

Polyhedron and Right angle · Right angle and Tetrahedron · See more »

Simplex

In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions.

Polyhedron and Simplex · Simplex and Tetrahedron · See more »

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).

Polyhedron and Symmetric graph · Symmetric graph and Tetrahedron · 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.

Polyhedron and Symmetry group · Symmetry group and Tetrahedron · 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.

Polyhedron and Tetrahedron · Tetrahedron and Tetrahedron · See more »

Three-dimensional space

Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameters) are required to determine the position of an element (i.e., point).

Polyhedron and Three-dimensional space · Tetrahedron and Three-dimensional space · See more »

Trapezohedron

The n-gonal trapezohedron, antidipyramid, antibipyramid or deltohedron is the dual polyhedron of an n-gonal antiprism.

Polyhedron and Trapezohedron · Tetrahedron and Trapezohedron · See more »

Uniform polyhedron

A uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other).

Polyhedron and Uniform polyhedron · Tetrahedron and Uniform polyhedron · See more »

Vertex (geometry)

In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet.

Polyhedron and Vertex (geometry) · Tetrahedron and Vertex (geometry) · 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.

Polyhedron and Vertex figure · Tetrahedron and Vertex figure · 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.

Polyhedron and Volume · Tetrahedron and Volume · See more »

The list above answers the following questions

Polyhedron and Tetrahedron Comparison

Polyhedron has 210 relations, while Tetrahedron has 202. As they have in common 40, the Jaccard index is 9.71% = 40 / (210 + 202).

References

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

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