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Topics referred to by the same term
Conway notation may refer to the following notations created by John Horton Conway: Conway chained arrow notation Conway notation (knot theory) Conway
Conway_notation
Method of describing higher-order polyhedra
In geometry and topology, Conway polyhedron notation, invented by John Horton Conway and promoted by George W. Hart, is used to describe polyhedra based
Conway_polyhedron_notation
Notation used to describe knots based on operations on tangles
In knot theory, Conway notation, invented by John Horton Conway, is a way of describing knots that makes many of their properties clear. It composes a
Conway_notation_(knot_theory)
Means of expressing certain extremely large numbers
Conway chained arrow notation, created by mathematician John Horton Conway, is a means of expressing certain extremely large numbers. It is simply a finite
Conway_chained_arrow_notation
Study of mathematical knots
Dowker–Thistlethwaite notation. The Conway notation for knots and links, named after John Horton Conway, is based on the theory of tangles (Conway 1970). The advantage
Knot_theory
English mathematician (1937–2020)
uniform polychoron. Conway also suggested a system of notation dedicated to describing polyhedra called Conway polyhedron notation. In the theory of tessellations
John_Horton_Conway
Near-miss Johnson solid with 92 faces
isosceles instead. The shape is a symmetrohedron with notation I(1,2,*,[2]) By Conway polyhedron notation, the dual polyhedron can be called a joined truncated
Rectified truncated icosahedron
Rectified_truncated_icosahedron
Geometric operation applied to a polyhedron
uniform polytopes. John Conway explored generalized polyhedron operators, defining what is now called Conway polyhedron notation, which can be applied to
Snub_(geometry)
Simplest non-trivial closed knot with three crossings
listed as 31 in the Alexander-Briggs notation. The Dowker notation for the trefoil is 4 6 2, and the Conway notation is [3]. The trefoil can be described
Trefoil_knot
Mathematical notation for describing the structure of knots
different number sequences possible in this notation. Alexander–Briggs notation Conway notation Gauss notation Dowker, C. H.; Thistlethwaite, Morwen B. (1983-07-01)
Dowker–Thistlethwaite notation
Dowker–Thistlethwaite_notation
Three linked but pairwise separated rings
Alexander–Briggs notation "63 2", meaning that this is the second of three 6-crossing 3-component links to be listed. The Conway notation for the Borromean
Borromean_rings
Notation for trigonometric relationships
In geometry, the Conway triangle notation simplifies and clarifies the algebraic expression of various trigonometric relationships in a triangle. Using
Conway_triangle_notation
Prime knot named for John Horton Conway
specifically in knot theory, the Conway knot (or Conway's knot) is a particular knot with 11 crossings, named after John Horton Conway. It is related by mutation
Conway_knot
Notation for 2-dimensional spherical, euclidean and hyperbolic symmetry groups
geometry, orbifold notation (or orbifold signature) is a system, invented by the mathematician William Thurston and promoted by John Conway, for representing
Orbifold_notation
Mathematical knot with crossing number 5
three-half twists. It is listed as the 52 knot in the Alexander-Briggs notation, and is one of two knots with crossing number five, the other being the
Three-twist_knot
Two interlinked loops with five structural crossings
each other by a geometric symmetry of the realization. In braid theory notation, the link is written σ12σ22σ1−1σ2−2. Its Alexander polynomial is
Whitehead_link
Simplest nontrivial knot link
Unknotting no. and problem Notation and operations Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister
Hopf_link
(knot theory) – a notation invented by Conway for describing knots in knot theory Conway polyhedron notation – notation invented by Conway used to describe
List of things named after John Horton Conway
List_of_things_named_after_John_Horton_Conway
Notation for mathematical knots
Computation. 105 (2–3): 271–289. doi:10.1016/S0096-3003(98)10106-6. MR 1710214. See p. 274 Conway notation (knot theory) Dowker–Thistlethwaite notation v t e
Gauss_notation
Topics referred to by the same term
Arrow notation may refer to: Conway chained arrow notation Knuth's up-arrow notation Arrow notation (Ramsey theory), or infinitary combinatorics Arrow
Arrow_notation
Approach to knot theory by John Conway
closures of rational tangles. One motivation for Conway's study of tangles was to provide a notation for knots more systematic than the traditional enumeration
Tangle_(mathematics)
Method of notation of very large integers
In mathematics, Knuth's up-arrow notation is a method of notation for very large integers, introduced by Donald Knuth in 1976. In his 1947 paper, R. L
Knuth's_up-arrow_notation
Polyhedron with parallel bases connected by triangles
by an alternating band of 2n triangles. They are represented by the Conway notation An. Antiprisms are a subclass of prismatoids, and are a (degenerate)
Antiprism
Mathematical knot with crossing number 5
three-twist knot. It is listed as the 51 knot in the Alexander-Briggs notation, and can also be described as the (5,2)-torus knot. The cinquefoil is the
Cinquefoil_knot
Unique knot with a crossing number of four
Δ(t)=−t+3−t−1, since (1−10−1) is a possible Seifert matrix, or because of its Conway polynomial, which is ∇(z)=1−z2, and the Jones polynomial is V(q)=q2−q+1−q−1+q−2
Figure-eight knot (mathematics)
Figure-eight_knot_(mathematics)
Motif with two doubly-interlinked loops
no. 4 Hyperbolic volume 0 Linking no. 2 Stick no. 5 Unknotting no. 2 Conway notation [4] Thistlethwaite L4a1 Last / Next L2a1 / L5a1 Other alternating
Solomon's_knot
Geometric operation on a regular polytope
regular polytope to its birectified form. Chamfer (geometry) Conway polyhedron notation Uniform 4-polytope Uniform polyhedron Coxeter, H.S.M. Regular
Cantellation_(geometry)
Loop seen as a trivial knot
but the Kinoshita–Terasaka knot and Conway knot (both of which have 11 crossings) have the same Alexander and Conway polynomials as the unknot. It is an
Unknot
Two-dimensional cellular automaton
Conway's Game of Life (sometimes abbreviated as CGoL) or simply Life, is a cellular automaton devised by the British mathematician John Horton Conway
Conway's_Game_of_Life
Type of polyhedron
George Hart's Conway interpreter: generates polyhedra in VRML, taking Conway notation as input, [1] VRML model Convex Polyhedra containing Golden Rhombi:
Expanded_icosidodecahedron
Polyhedron with 7 faces
Virtual Reality Polyhedra www.georgehart.com: The Encyclopedia of Polyhedra Conway Notation for Polyhedra Try: "Y6" [1] Hexagonal pyramid - Polytope Wiki
Hexagonal_pyramid
Polyhedron made by cutting off a trapezohedron's polar vertices
America. p. 52. ISBN 978-1-4704-7184-2. Alsina & Nelsen (2023), p. 53. Conway Notation for Polyhedra Try: "tndAn", where n=4,5,6... example "t5dA5" is a dodecahedron
Truncated_trapezohedron
Polyhedron with 10 faces
Polyhedra www.georgehart.com: The Encyclopedia of Polyhedra VRML model Archived 2018-02-24 at the Wayback Machine Conway Notation for Polyhedra Try: "dA5"
Pentagonal_trapezohedron
Archimedean solid with 62 faces
Elements F = 62, E = 120, V = 60 (χ = 2) Faces by sides 20{3}+30{4}+12{5} Conway notation eD or aaD Schläfli symbols rr{5,3} or r{53} t0,2{5,3} Wythoff symbol
Rhombicosidodecahedron
Mathematical knot with crossing number 7
Hyperbolic volume 5.13794 Stick no. 9 Unknotting no. 2 Conway notation [313] A–B notation 74 Dowker notation 6, 10, 12, 14, 4, 2, 8 Last / Next 73 / 75 Other
74_knot
Catalan solid with 24 kite faces
octahedron divides its equilateral triangles into kite faces. In Conway polyhedron notation this represents an ortho operation to a cube or octahedron. The
Deltoidal_icositetrahedron
Polyhedron made of 12 congruent kites
twelve faces which are congruent kites. It can be described by the Conway notation dA6. It is an isohedral (face-transitive) figure, meaning that all
Hexagonal_trapezohedron
Coxeter, Regular and Semi-Regular Polytopes II, Coxeter notation for 4D point groups 2003 John Conway and Smith, On Quaternions and Octonions, Completed quaternion-based
Point groups in four dimensions
Point_groups_in_four_dimensions
Type of polyhedron
Symmetries of Things 2008, ISBN 978-1-56881-220-5 George Hart's Conway interpreter: generates polyhedra in VRML, taking Conway notation as input v t e
Truncated rhombicosidodecahedron
Truncated_rhombicosidodecahedron
Non-trivial knot which cannot be written as the knot sum of two non-trivial knots
Unknotting no. and problem Notation and operations Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister
Prime_knot
Origin and evolution of the symbols used to write equations and formulas
including the Conway chained arrow notation, the Conway notation of knot theory, and the Conway polyhedron notation. The Coxeter notation system classifies
History of mathematical notation
History_of_mathematical_notation
Catalan solid with 24 faces
Polyhedra www.georgehart.com: The Encyclopedia of Polyhedra VRML model Archived 2018-10-11 at the Wayback Machine Conway Notation for Polyhedra Try: "dtC"
Triakis_octahedron
Mathematical knot with crossing number 6
knot. The stevedore knot is listed as the 61 knot in the Alexander–Briggs notation, and it can also be described as a twist knot with four half twists, or
Stevedore_knot_(mathematics)
Polynomial invariant of framed links
Unknotting no. and problem Notation and operations Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister
Bracket_polynomial
Group whose operation is a composition of braids
Unknotting no. and problem Notation and operations Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister
Braid_group
Integer-valued knot invariant; least number of crossings in a knot diagram
Unknotting no. and problem Notation and operations Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister
Crossing_number_(knot_theory)
The Symmetries of Things 2008, ISBN 978-1-56881-220-5 George Hart's Conway interpreter: generates polyhedra in VRML, taking Conway notation as input
Snub_rhombicuboctahedron
Type of polyhedron
truncating the vertices down to the midpoint of the original edges. In Conway polyhedron notation, it is represented as aPn, an ambo-prism. The lateral squares
Rectified_prism
Knot invariant
knot polynomial, in 1923. In 1969, John Conway showed a version of this polynomial, now called the Alexander–Conway polynomial, could be computed using a
Alexander_polynomial
Solid with 2 parallel n-gonal bases connected by n parallelograms
char. 2 Vertex configuration 4.4.n Schläfli symbol {n}×{ } t{2,n} Conway notation Pn Coxeter diagram Symmetry group Dnh, [n,2], (*n22), order 4n Rotation
Prism_(geometry)
Archimedean solid with 14 faces
The Uniform Polyhedra Virtual Reality Polyhedra www.georgehart.com: The Encyclopedia of Polyhedra VRML model Conway Notation for Polyhedra Try: "tC"
Truncated_cube
Knot that can't be tied in a string of constant diameter
Unknotting no. and problem Notation and operations Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister
Wild_knot
Mathematical knot with crossing number 7
) = 3 t − 5 + 3 t − 1 , {\displaystyle \Delta (t)=3t-5+3t^{-1},\,} its Conway polynomial is ∇ ( z ) = 3 z 2 + 1 , {\displaystyle \nabla (z)=3z^{2}+1,\
7_2_knot
Arithmetic operation
repeated, exponentiation. There is no universal notation for tetration, though Knuth's up arrow notation a↑↑n and the left-exponent na are common. Under
Tetration
Prime knot with crossing number 10
Newton Little's table. This duplication had been missed by John Horton Conway several years before in his knot table and subsequently found its way into
Perko_pair
Mathematical knot with crossing number 6
− t − 2 , {\displaystyle \Delta (t)=-t^{2}+3t-3+3t^{-1}-t^{-2},\,} its Conway polynomial is ∇ ( z ) = − z 4 − z 2 + 1 , {\displaystyle \nabla (z)=-z^{4}-z^{2}+1
62_knot
Geodesic polyhedron with 180 faces
archived from the original on July 4, 2008 Reprinted by Dover 1999 ISBN 978-0-486-40921-4 VTML polyhedral generator Try "ktI" (Conway polyhedron notation)
Hexapentakis truncated icosahedron
Hexapentakis_truncated_icosahedron
Property in knot theory
Unknotting no. and problem Notation and operations Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister
Tricolorability
Convex polyhedron with 92 faces
Symmetries of Things 2008, ISBN 978-1-56881-220-5 George Hart's Conway interpreter: generates polyhedra in VRML, taking Conway notation as input v t e
Rectified truncated dodecahedron
Rectified_truncated_dodecahedron
Catalan solid with 24 faces
of Polyhedra VRML model Archived 2021-11-22 at the Wayback Machine Conway Notation for Polyhedra Try: "dtO" or "kC" Tetrakis Hexahedron – Interactive
Tetrakis_hexahedron
Unknotting no. and problem Notation and operations Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister
Bridge_number
Catalan solid with 60 faces
people play on are Pentakis Dodecahedra, or at least elevated dodecahedra. Conway, John H.; Burgiel, Heidi; Goodman-Strauss, Chaim (2008). "Chapter 21: Naming
Pentakis_dodecahedron
Classification of a two-dimensional repetitive pattern
full notation. The remaining names are p1, p2, p3, p3m1, p31m, p4, and p6. Orbifold notation for wallpaper groups, advocated by John Conway (Conway, 1992)
Wallpaper_group
Catalan solid with 120 faces
each triangle face vertex. This is *n32 in orbifold notation, and [n,3] in Coxeter notation. Conway, Symmetries of things, p.284 "DisdyakisTriacontahedron"
Disdyakis_triacontahedron
Convex polyhedron with 38 faces
Symmetries of Things 2008, ISBN 978-1-56881-220-5 George Hart's Conway interpreter: generates polyhedra in VRML, taking Conway notation as input v t e
Rectified_truncated_cube
Convex polyhedron with 90 rhombic faces
edges are equal length. This construction is expressed in the Conway polyhedron notation jtI with join operator j. Without the equal edge constraint, the
Rhombic_enneacontahedron
here for quick comparison of their properties and varied naming schemes. Conway knot 11n34 Kinoshita–Terasaka knot 11n42 List of knots List of mathematical
List_of_prime_knots
Truncated trapezohedron with a 6-sided base
space-filling honeycomb along with an irregular dodecahedron. Goldberg polyhedron Wearie-Phelan Bubbles Conway Notation for Polyhedra Try: "t6dA6". v t e
Truncated hexagonal trapezohedron
Truncated_hexagonal_trapezohedron
Fundamental group of a knot complement
Unknotting no. and problem Notation and operations Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister
Knot_group
Normalized hyperbolic volume of the complement of a hyperbolic knot
Unknotting no. and problem Notation and operations Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister
Hyperbolic_volume
Knot which lies on the surface of a torus in 3-dimensional space
Unknotting no. and problem Notation and operations Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister
Torus_knot
Concept in knot theory
In mathematical knot theory, a Conway sphere, named after John Horton Conway, is a 2-sphere intersecting a given knot or link in a 3-manifold transversely
Conway_sphere
Link that consists of finitely many unlinked unknots
Crossing no. 0 Linking no. 0 Stick no. 6 Unknotting no. 0 Conway notation - A–B notation 02 1 Dowker notation - Next L2a1 Other , tricolorable (if n>1)
Unlink
Attempt to classify and tabulate all possible knots
Unknotting no. and problem Notation and operations Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister
Knot_tabulation
Convex polyhedron with 38 faces
Symmetries of Things 2008, ISBN 978-1-56881-220-5 George Hart's Conway interpreter: generates polyhedra in VRML, taking Conway notation as input v t e
Rectified truncated octahedron
Rectified_truncated_octahedron
Family of mathematical knots
{n}{2}}t+(n+1)-{\frac {n}{2}}t^{-1}&{\text{if }}n{\text{ is even,}}\\\end{cases}}} and the Conway polynomial is ∇ ( z ) = { n + 1 2 z 2 + 1 if n is odd 1 − n 2 z 2 if
Twist_knot
Interlinked multi-loop construction where cutting one loop frees all the others
Unknotting no. and problem Notation and operations Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister
Brunnian_link
Collection of knots that do not intersect, but may be linked
Unknotting no. and problem Notation and operations Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister
Link_(knot_theory)
than a decimal numeric representation, although longer than scientific notation. Two naming scales for large numbers have been used in English and other
Names_of_large_numbers
Knot invariant that is a polynomial
Alexander polynomial. Alexander–Briggs notation organizes knots by their crossing number. Alexander polynomials and Conway polynomials can not recognize the
Knot_polynomial
Convention where symbols represent concepts
Set-builder notation, a formal notation for defining sets in set theory Systems to represent very large numbers Conway chained arrow notation, an arrow
Notation_system
Every knot or link can be represented as a closed braid
Unknotting no. and problem Notation and operations Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister
Alexander's_theorem
Type of mathematical link
Unknotting no. and problem Notation and operations Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister
Hyperbolic_link
Orientable surface whose boundary is a knot or link
Unknotting no. and problem Notation and operations Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister
Seifert_surface
Mathematical invariant of a knot or link
and require other invariants to distinguish them. Examples include the Conway knot and the Kinoshita-Terasaka knot, with 11 crossings. HOMFLY polynomial
Jones_polynomial
Archimedean solid with 62 faces
F = 62, E = 180, V = 120 (χ = 2) Faces by sides 30{4}+20{6}+12{10} Conway notation bD or taD Schläfli symbols tr{5,3} or t{53} t0,1,2{5,3} Wythoff symbol
Truncated_icosidodecahedron
Embedding of the circle in three dimensional Euclidean space
this bracket operation is that it produces knots with a trivial Alexander–Conway polynomial; specifically, ∇([α,β])=1. The article also establishes a relationship
Knot_(mathematics)
One of three types of isotopy-preserving local changes to a knot diagram
Unknotting no. and problem Notation and operations Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister
Reidemeister_move
Mathematical knot with crossing number 7
{\displaystyle \Delta (t)=t^{3}-t^{2}+t-1+t^{-1}-t^{-2}+t^{-3},\,} its Conway polynomial is ∇ ( z ) = z 6 + 5 z 4 + 6 z 2 + 1 , {\displaystyle \nabla
71_knot
Polynomial invariant arising in knot theory
Józef H. Przytycki; .Paweł Traczyk (1987). "Invariants of Links of Conway Type". Kobe J. Math. 4: 115–139. arXiv:1610.06679. Ramadevi, P.; Govindarajan
HOMFLY_polynomial
Type of knot
other knots. Caveat Spills if the standing part is pulled forcibly in the wrong direction ABoK #4, #46, #514, #515, #519 Conway Notation 3 A/B notation 31
Overhand_knot
Type of stopper knot used in sailing and climbing
General-purpose stopper knot. Replaces the common overhand knot in many uses. ABoK #420 #520 #570 Conway Notation 2 2 A/B notation 41 Instructions [1]
Figure-eight_knot
Connected sum of two trefoil knots with same chirality
the square of the Alexander polynomial of a trefoil knot. Similarly, the Conway polynomial of a granny knot is ∇ ( z ) = ( z 2 + 1 ) 2 . {\displaystyle
Granny_knot_(mathematics)
Type of knot in knot theory
lens space. The names rational knot and rational link were coined by John Conway who defined them as arising from numerator closures of rational tangles
2-bridge_knot
Type of polyhedron
ISBN 978-1-56881-220-5 George Hart's Conway interpreter: generates polyhedra in VRML, taking Conway notation as input Prism Expansions [1] Toroid model
Truncated_rhombicuboctahedron
Mathematical tool for studying knots
each other only in a small region. For some knot polynomials, such as the Conway, Alexander, and Jones polynomials, the relevant skein relations are sufficient
Skein_relation
Catalan solid with 24 faces
duals to the uniform polyhedra related to the cube and regular octahedron. Conway, Symmetries of things, p.284 "Promorphology of Crystals I". "Crystal Form
Pentagonal_icositetrahedron
Type of polyhedron
George Hart's Conway interpreter: generates polyhedra in VRML, taking Conway notation as input Variations on a Rhombic Theme www.software3d.com: Prism-Expanded
Expanded_cuboctahedron
Type of mathematical knot
828122 Unknotting no. 5 Conway notation [−2,3,7] Dowker notation 4, 8, -16, 2, -18, -20, -22, -24, -6, -10, -12, -14 D–T notation 12n242 Last / Next 12n241
(−2,3,7)_pretzel_knot
Polyhedron with 8 triangles and 6 squares
24 Vertices 12 Vertex configuration 3.4.3.4 Schläfli symbol r{4,3} Conway notation aC Coxeter diagram Symmetry group Octahedral Oh Dihedral angle (degrees)
Cuboctahedron
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