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Torus

In geometry, a torus (pl.: tori or toruses) is a surface of revolution generated by revolving a circle in three-dimensional space one full revolution about an axis that is coplanar with the circle. The main types of tori include ring tori, horn tori, and spindle tori. A ring torus is sometimes colloquially referred to as a doughnut.

Products, Topology & N-dimensional torus

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Overview

Geometry

Topology

Two-sheeted cover

N-dimensional torus

Flat torus

Genus g surface

Toroidal polyhedra

Automorphisms

Coloring a torus

De Bruijn torus

Cutting a torus

  • OEIS On-Line Encyclopedia of Integer Sequences

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Map overview Semantic statistics

Torus

Nodes171
Edges170
Triples128
Avg. degree1.99
Density0.011696
Components1

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Torus

Top relations

related to External links · 18
Torus → Anders Sandberg, Brady Haran, Carlo, Creation, February, Fly-through, Ghostarchive, January, July, Numberphile, Relational Perspective Map, Retrieved, Séquin, Topology, Torus Earth, Twisted Torus, Visualizing, Wayback Machine
related to Conformal classification of flat tori · 14
Torus → As, Bonnet, Due, Gauss, Gaussian, In, It, One, Riemann, Such, The, The Uniformization, Then, This
related to Flat torus · 12
Torus → Cartesian, Euclidean, Gaussian, In, It, Its, Lie, Perhaps, R2, Riemannian, This, Z2
related to n-dimensional torus · 12
Torus → And, Equivalently, Just, Rn, S1, T1, T2, That, The, This, Tn, Zn
related to Topology · 11
Torus → C2, Clifford, Hopf, In, R3, S1, S2, S3, The, This, Topologically
is a · 10
Torus → array of symbols from an alphabet, closed surface defined as the product of two circles, Eilenberg, free abelian group of rank n, free abelian group of rank n choose k, n-fold product of the circle, product of two circles, torus plus the volume inside the torus, torus with the metric inherited from its representation as the quotient, twofold branched cover of the 2-sphere
related to Configuration space · 8
Torus → As, For, Möbius, S1, Sn, Symbolically, The, Tn
related to Genus g surface · 6
Torus → And, As, In, That, The, To
related to Coloring a torus · 5
Torus → Contrast, Equivalently, Heawood, Since, The
related to de Bruijn torus · 5
Torus → Bruijn, De Bruijn, In, It, Its

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Important terminology

surface circle one displaystyle space ring genus two flat tori axis group also quotient compact revolution product toroidal topology sphere

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Torusis atorus plus the volume inside the torus0.90text
Torusis aproduct of two circles0.90text
Torusis aclosed surface defined as the product of two circles0.90text
Torusis atwofold branched cover of the 2-sphere0.90text
Torusis afree abelian group of rank n0.90text
Torusis afree abelian group of rank n choose k0.90text
Torusis an-fold product of the circle0.90text
Torusis atorus with the metric inherited from its representation as the quotient0.90text
Torusis aEilenberg0.90text
Torusis aarray of symbols from an alphabet0.90text
rubberinstance ofThe surface of a coffee cup and a doughnut are both topological tori with genus one.An example of a torus can be constructed by taking a rectangular strip of flexible material0.80text
and joining the top edge to the bottom edgeinstance ofThe surface of a coffee cup and a doughnut are both topological tori with genus one.An example of a torus can be constructed by taking a rectangular strip of flexible material0.80text

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