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...

its faces. The great rhombic triacontahedron is a nonconvex isohedral, isotoxal polyhedron with 30 intersecting rhombic faces. The rhombic hexecontahedron...

constructed by four mirrors can alternate long and short edges, and d8, an isotoxal octagon constructed with equal edge lengths, but vertices alternating two...

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...

the decorative motifs in girih tiles. An isotoxal polygon has two vertices and one edge. There are isotoxal decagram forms, which alternates vertices...

constructed by three mirrors can alternate long and short edges, and d6, an isotoxal hexagon constructed with equal edge lengths, but vertices alternating two...

{5} has density 1. Isotoxal tetradecagon, {(7/2)α}, has density 2, similar to regular {7/2}. Heptagram {7/3} has density 3. Isotoxal hexagram (compound)...

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...

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

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...

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...

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...

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...

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...

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...

properties §6.2 Isohedral tiling, §6.3 isogonal tiling, §6.4 isotoxal tiling, list of isotoxal tilings, §6.5 striped pattern, §6.6 Evgraf Fedorov, Alexei...

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...

defined as a parallelogram with equal diagonals that bisect the angles. If a figure is both a rectangle (right angles) and a rhombus (equal edge lengths), then...

criterion ) with β 3 = { 0 , 1 } {\displaystyle \beta _{3}=\{0,1\}} and the isotoxal (equilateral) hexagons of the Capurso criterion with χ 3 = { 1 , − 1 }...

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...

Each vertex is surrounded by 3 octahedra and 2 tetrahedra; the vertex figure is a triangular prism. Topologically, under its highest symmetry, [3,3,3]...

group O, [4,3]+, (432) Dihedral angle 120° Properties convex, face-transitive isohedral, isotoxal, parallelohedron Cuboctahedron (dual polyhedron) Net...