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Concept
Isotoxal figure
Summary
In geometry, a polytope (for example, a polygon or a polyhedron) or a tiling is isotoxal () 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.
Isotoxal polygons
An isotoxal polygon is an even-sided i.e. equilateral polygon, but not all equilateral polygons are isotoxal. The duals of isotoxal polygons are isogonal polygons. Isotoxal 4n-gons are centrally symmetric, so are also zonogons.
In general, an isotoxal 2n-gon has \mathrm{D}_n, (^*nn) dihedral symmetry. For example, a rhombus is an isotoxal "2×2-gon" (quadrilateral) with \mathrm{D}_2, (^*22) symmetry. All regular polygons (equilateral triangle, square, etc.) are isotoxal, having double t
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