In geometry, a polytope (e.g. a polygon or polyhedron) or a tiling is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries...
Isogonal, a mathematical term meaning "having similar angles", may refer to: Isogonal figure or polygon, polyhedron, polytope or tiling Isogonal trajectory...
In geometry, the isogonal conjugate of a point P with respect to a triangle △ABC is constructed by reflecting the lines PA, PB, PC about the angle bisectors...
vertex-transitive, i.e. isogonal. The Catalan solids, the bipyramids, and the trapezohedra are all isohedral. They are the duals of the (isogonal) Archimedean solids...
called isogonal lines, will also have interesting properties. For instance, if three cevians of a triangle intersect at a point P, then their isogonal lines...
equal (that is, if it is also equilateral) then it is a regular polygon. Isogonal polygons are equiangular polygons which alternate two edge lengths. For...
intersects the given curves by an arbitrary (but fixed) angle, one gets an isogonal trajectory. Generally, one assumes that the pencil of curves is given implicitly...
in the internal angle, α. {∞α} is the dual polygon of an isogonal skew apeirogon. An isogonal skew apeirogon alternates two types of edges with various...
If there are k orbits of vertices, a tiling is known as k-uniform or k-isogonal; if there are t orbits of tiles, as t-isohedral; if there are e orbits...
Unicode glyph ۞ at U+06DE. Deeper truncations of the square can produce isogonal (vertex-transitive) intermediate star polygon forms with equal spaced vertices...
truncations of the regular pentadecagon and pentadecagrams can produce isogonal (vertex-transitive) intermediate star polygon forms with equal spaced vertices...
equilateral polygons are isotoxal. The duals of isotoxal polygons are isogonal polygons. Isotoxal 4 n {\displaystyle 4n} -gons are centrally symmetric...
not lie on any of the extended sides BC, CA, AB, and let P −1 denote the isogonal conjugate of P. The pedal triangle of P is homothetic to the antipedal...
tilings are isogonal and monohedral. A semi-regular (or Archimedean) tessellation uses more than one type of regular polygon in an isogonal arrangement...
omnitruncated icosahedron is an Archimedean solid, one of thirteen convex, isogonal, non-prismatic solids constructed by two or more types of regular polygon...
dodecagram can be seen as a quasitruncated hexagon, t{6/5}={12/5}. Other isogonal (vertex-transitive) variations with equally spaced vertices can be constructed...
circumcircle. Tangential: all sides are tangent to an inscribed circle. Isogonal or vertex-transitive: all corners lie within the same symmetry orbit. The...
rhombicosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon...
conjugates of circumconics are lines. (This property holds for isogonal conjugates as well.) Isogonal conjugate Triangle center Robert Lachlan, An Elementary...
B, C respectively. The isogonal conjugate of P is sometimes denoted by P*. The isogonal conjugate of P* is P. A self-isogonal cubic is a triangle cubic...
figures. Vertex figures are especially significant for uniforms and other isogonal (vertex-transitive) polytopes because one vertex figure can define the...
gyration orders. The most common high symmetry hexadecagons are d16, an isogonal hexadecagon constructed by eight mirrors can alternate long and short edges...
Deeper truncations of the regular dodecagon and dodecagrams can produce isogonal (vertex-transitive) intermediate star polygon forms with equal spaced vertices...
directed edges. The highest symmetry irregular tetradecagons are d14, an isogonal tetradecagon constructed by seven mirrors which can alternate long and...
tangent to this hyperbola at I {\displaystyle I} . The hyperbola is the isogonal conjugate of O I {\displaystyle OI} , the line joining the circumcenter...
as directed edges. The highest symmetry irregular icosagons are d20, an isogonal icosagon constructed by ten mirrors which can alternate long and short...
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