This article is about geometry. For edge transitivity in graph theory, see Edge-transitive graph.
In geometry, a polytope (for example, a polygon or a polyhedron) or a tiling is isotoxal (from Greek τόξον 'arc') or edge-transitive if its symmetries act transitively on its edges. Informally, this means that there is only one type of edge to the object: given two edges, there is a translation, rotation, and/or reflection that will move one edge to the other while leaving the region occupied by the object unchanged.
geometry, a polytope (for example, a polygon or a polyhedron) or a tiling is isotoxal (from Greek τόξον 'arc') or edge-transitive if its symmetries act transitively...
figure constructed only from regular polygons. They can be represented visually with colors by different uniform colorings. Edge-transitive (Isotoxal...
2-dimensional figure is isotoxal, i.e. edge-transitive. An isotopic 3-dimensional figure is isohedral, i.e. face-transitive. An isotopic 4-dimensional figure is...
constructed by four mirrors can alternate long and short edges, and d8, an isotoxal octagon constructed with equal edge lengths, but vertices alternating two...
its faces. The great rhombic triacontahedron is a nonconvex isohedral, isotoxal polyhedron with 30 intersecting rhombic faces. The rhombic hexecontahedron...
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, alternating vertices at...
constructed by three mirrors can alternate long and short edges, and d6, an isotoxal hexagon constructed with equal edge lengths, but vertices alternating two...
and vice versa. The dual of an isotoxal polyhedron (one in which any two edges are equivalent [...]) is also isotoxal. Duality is closely related to polar...
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...
by five mirrors which can alternate long and short edges, and p10, an isotoxal decagon, constructed with equal edge lengths, but vertices alternating...
within the same symmetry orbit. The polygon is also cyclic and equiangular. Isotoxal or edge-transitive: all sides lie within the same symmetry orbit. The polygon...
pentagram. The next one is the {8/3} octagram and its related {8/2} star figure (a compound of two squares), followed by the regular enneagram, which also...
(vertex-transitive) polygon is an isotoxal (edge-transitive) polygon. For example, the (isogonal) rectangle and (isotoxal) rhombus are duals. In a cyclic...
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...
dodecagon, or 12-gon, is any twelve-sided polygon. A regular dodecagon is a figure with sides of the same length and internal angles of the same size. It has...
represented by its Schläfli symbol {5/2}. A similar figure to the pentagram is a five-pointed simple isotoxal star ☆ without self-intersecting edges. It is...
orbits of tiles, as t-isohedral; if there are e orbits of edges, as e-isotoxal. k-uniform tilings with the same vertex figures can be further identified...
understand it: one could "perceive that the word 'chiliagon' signifies a figure with a thousand angles [but] that is just the meaning of the term, and it...
Since each vertex of a tesseract is adjacent to four edges, the vertex figure of the tesseract is a regular tetrahedron. The dual polytope of the tesseract...
equilateral triangles, and the third a compound of three pentagrams. The compound figure {15/3} can be loosely seen as the two-dimensional equivalent of the 3D compound...
icosidodecahedron is the great rhombic triacontahedron; it is nonconvex, isohedral and isotoxal. It has 30 intersecting rhombic faces. It can also be called the great...
but is not necessarily vertex-transitive. Isogonal: vertex-transitive. Isotoxal: edge-transitive. Isohedral: face-transitive. Noble: face-transitive and...
{11/4} and {11/5} Dodecagram – {12/5} m and n must be coprime, or the figure will degenerate. The degenerate regular stars of up to 12 sides are: Tetragon...
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