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isotoxal figure : ウィキペディア英語版
isotoxal figure
:''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 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.
The term ''isotoxal'' is derived from the Greek τοξον meaning ''arc''.
== Isotoxal polygons ==
An isotoxal polygon is an equilateral polygon, but not all equilateral polygons are isotoxal. The dual of isotoxal polygons are isogonal polygons.
In general, an isotoxal ''2n''-gon will have Dn (
*nn) dihedral symmetry. A rhombus is an isotoxal polygon with D2 (
*22) symmetry.
All regular polygons (equilateral triangle, square, etc.) are isotoxal, having double the minimum symmetry order: a regular ''n''-gon has Dn (
*nn) dihedral symmetry. A regular 2''n''-gon is an isotoxal polygon and can be marked with alternately colored vertices, removing the line of reflection through the mid-edges.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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