hasSymmetryType
P60479
predicate
Indicates that one entity possesses a specific kind or pattern of symmetry characterized or classified by the other entity.
Observed surface forms (12)
- hasSymmetryProperty ×17
- symmetryType ×6
- symmetryClass ×3
- hasSymmetryClass ×2
- axialSymmetryStatus ×1
- boardSymmetry ×1
- hasGeodesicSymmetry ×1
- hasSupersymmetryType ×1
- hasSymmetryGroupType ×1
- hasTypicalSymmetryClassLabel ×1
- haveSymmetryGroup ×1
- typeOfSymmetry ×1
Sample triples (43)
| Subject | Object |
|---|---|
| Bernstein polynomials | B_{n,k}(x) = B_{n,n-k}(1-x) via predicate surface "hasSymmetryProperty" ⓘ |
| Circle Limit I | reflection symmetry via predicate surface "symmetryType" ⓘ |
| Circle Limit I | rotational symmetry via predicate surface "symmetryType" ⓘ |
| Conway’s soldiers | translation-invariant in horizontal directions via predicate surface "boardSymmetry" ⓘ |
| Eightfold Way | internal symmetry ⓘ |
| Euler’s reflection formula | reflection across the line Re(z) = 1/2 via predicate surface "typeOfSymmetry" ⓘ |
| Fano plane | flag-transitive via predicate surface "hasSymmetryProperty" ⓘ |
| Fano plane | line-transitive via predicate surface "hasSymmetryProperty" ⓘ |
| Fano plane | point-transitive via predicate surface "hasSymmetryProperty" ⓘ |
| Gaussian orthogonal ensemble | orthogonal symmetry via predicate surface "symmetryClass" ⓘ |
| Gaussian symplectic ensemble | class AII in Altland–Zirnbauer classification via predicate surface "hasTypicalSymmetryClassLabel" NERFINISHED ⓘ |
| Gaussian symplectic ensemble | symplectic symmetry via predicate surface "hasSymmetryClass" ⓘ |
| Gaussian unitary ensemble | unitary symmetry via predicate surface "symmetryClass" ⓘ |
| Ginibre ensemble | non-Hermitian via predicate surface "symmetryClass" ⓘ |
| Great Parterre | bilateral symmetry ⓘ |
| Greek cross | bilateral symmetry ⓘ |
| Greek cross | radial symmetry ⓘ |
|
Hurwitz surfaces
surface form:
Hurwitz surface
|
maximally symmetric for its genus ⓘ |
| Jacobi ensemble | orthogonal/unitary/symplectic depending on β via predicate surface "hasSymmetryClass" ⓘ |
| Jacobi polynomials | P_n^{(α,β)}(-x) = (-1)^n P_n^{(β,α)}(x) via predicate surface "hasSymmetryProperty" ⓘ |
|
Johnson solids are not vertex-transitive
surface form:
Johnson solids
|
generally low symmetry via predicate surface "hasSymmetryProperty" ⓘ |
|
Johnson solids are not vertex-transitive
surface form:
Johnson solids
|
not vertex-transitive via predicate surface "hasSymmetryProperty" ⓘ |
| Kayles | positions symmetric under reflection of the row via predicate surface "hasSymmetryProperty" ⓘ |
| Kepler–Poinsot polyhedra | icosahedral symmetry via predicate surface "haveSymmetryGroup" ⓘ |
| Leech lattice | highly symmetric via predicate surface "hasSymmetryProperty" ⓘ |
| Møller scattering | crossing symmetry with Bhabha scattering via predicate surface "hasSymmetryProperty" ⓘ |
| Nil geometry | anisotropic ⓘ |
| Penrose tilings | decagonal symmetry via predicate surface "symmetryType" ⓘ |
| Penrose tilings | fivefold rotational symmetry via predicate surface "symmetryType" ⓘ |
| Poincaré upper half-plane model | reflections in geodesics are isometries via predicate surface "hasGeodesicSymmetry" ⓘ |
| Pythagorean triples | (a,b,c) and (b,a,c) represent the same triple geometrically via predicate surface "hasSymmetryProperty" ⓘ |
| S^2 × R geometry | product of spherical and Euclidean symmetries ⓘ |
| Schwinger model | broken by anomaly via predicate surface "axialSymmetryStatus" ⓘ |
| SymTridiagonal | HermitianForComplexEltype via predicate surface "symmetryType" ⓘ |
| Taj Mahal gardens in Agra | bilateral symmetry via predicate surface "symmetryType" ⓘ |
| Type I supergravity | minimal supersymmetry in ten dimensions via predicate surface "hasSupersymmetryType" ⓘ |
| Vandermonde's identity | symmetric in m and n via predicate surface "hasSymmetryProperty" ⓘ |
| Wigner 3j symbols | invariance under even permutations of columns via predicate surface "hasSymmetryProperty" ⓘ |
| Wigner 3j symbols | phase factor under column permutations via predicate surface "hasSymmetryProperty" ⓘ |
| Wigner 3j symbols | sign change under odd permutations of columns via predicate surface "hasSymmetryProperty" ⓘ |
| Wythoff Nim | P-positions are symmetric under exchanging the two piles via predicate surface "hasSymmetryProperty" ⓘ |
| anti-de Sitter space | non-compact Lie group via predicate surface "hasSymmetryGroupType" ⓘ |
| baryon decuplet | totally symmetric in flavor-spin-space for quarks via predicate surface "hasSymmetryProperty" ⓘ |