polyhedron) or a tiling is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure. This implies that each vertex...

Isogonal, a mathematical term meaning "having similar angles", may refer to: Isogonal figure or polygon, polyhedron, polytope or tiling Isogonal trajectory...

isotopic figure is an n-dimensional polytope or honeycomb with its facets ((n−1)-faces) congruent and transitive. The dual of an isotope is an isogonal polytope...

other isogonal (vertex-transitive) polytopes because one vertex figure can define the entire polytope. For polyhedra with regular faces, a vertex figure can...

isogon may refer to: Isogonal figure - a polygon or polyhedron with all of its vertices equivalent under the symmetries of the figure. A type of contour...

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...

equilateral polygons are isotoxal. The duals of isotoxal polygons are isogonal polygons. Isotoxal 4 n {\displaystyle 4n} -gons are centrally symmetric...

Deeper truncations of the regular dodecagon and dodecagrams can produce isogonal (vertex-transitive) intermediate star polygon forms with equal spaced vertices...

letter and group order. r12 is full symmetry, and a1 is no symmetry. p6, an isogonal hexagon constructed by three mirrors can alternate long and short edges...

ISBN 978-1-107-10340-5. See 11.3 Pyramids, Prisms, and Antiprisms, Figure 11.3b. Grünbaum, Branko (1997). "Isogonal Prismatoids". Discrete & Computational Geometry. 18:...

}}\triangle BCG)={\tfrac {1}{3}}({\text{Area of }}\triangle ABC).} The isogonal conjugate of a triangle's centroid is its symmedian point. Any of the three...

truncations of the regular pentadecagon and pentadecagrams can produce isogonal (vertex-transitive) intermediate star polygon forms with equal spaced vertices...

ABCDEF and the line EF are isogonal lines of ∠BEC, that is, each line is a reflection of the other about the angle bisector. (Figure 2) Triangles △EDF, △NPM...

rhombicosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon...

A hexagram (Greek) or sexagram (Latin) is a six-pointed geometric star figure with the Schläfli symbol {6/2}, 2{3}, or {{3}}. Since there are no true regular...

symmetry is labeled a1. The most common high symmetry octagons are p8, an isogonal octagon constructed by four mirrors can alternate long and short edges...

as directed edges. The highest symmetry irregular decagons are d10, an isogonal decagon constructed by five mirrors which can alternate long and short...

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...

equiangular: all its corner angles are equal (each of 90 degrees). It is isogonal or vertex-transitive: all corners lie within the same symmetry orbit. It...

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...

self-dual. The dual of an isogonal (vertex-transitive) polygon is an isotoxal (edge-transitive) polygon. For example, the (isogonal) rectangle and (isotoxal)...

tiling, which combine together as a chamfered square tiling. The vertex figure for this honeycomb is a disphenoid tetrahedron, and it is also the Goursat...

Symmetry group Dihedral (D11), order 2×11 Internal angle (degrees) ≈147.273° Properties Convex, cyclic, equilateral, isogonal, isotoxal Dual polygon Self...

circumcircle. Tangential: all sides are tangent to an inscribed circle. Isogonal or vertex-transitive: all corners lie within the same symmetry orbit. The...

(any two vertices can be transformed into each other by a symmetry of the figure). List of regular polytopes and compounds § Stars Wikimedia Commons has...

polychoron is isogonal and has 2p p-gonal prisms and p2 rectangular trapezoprisms (a cube with D2d symmetry) but cannot be made uniform. The vertex figure is a...

polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other). It follows...

intersecting line segments are removed from a regular star n-gon, the resulting figure is no longer regular, but can be seen as an isotoxal concave simple 2n-gon...

Mathematical Association of America, p. 85. Grünbaum, Branko (1997), "Isogonal Prismatoids", Discrete & Computational Geometry, 18: 13–52, doi:10.1007/PL00009307...