File talk:Crossed rectangles.png

This shape is also known as an angular "eight". "Bow-tie quadrilateral" also appears in searches. Not all bow-tie quadrilaterals are regular, so this one is a regular bow-tie (quadrilateral). The only support I have found for calling this shape a crossed-rectangle are mirrors of WP

Perhaps I missed an independent source that calls this shape a "crossed rectangle", but I can find no source that anyone considers them to be rectangles. Nor is there any source for this usage of "complex rectangles". In computer graphics, it seems complex rectangles are "filled-in rectangles" (not just the perimeter).

"Butterfly rectangle" also has a sourcing problem.

It seems to me that "crossed-rectangles" are given that name because a 3 dimensional wire-frame rectangle that has been twisted would have that shape. A twisted shape is no longer the same shape it started as. "Crossed rectangles" (note past tense), it would seem, are no longer rectangles, just as one folded in half would no longer be a rectangle (becoming either a triangle or an open shape.

The best I can find is this: "An equiangular quadrilateral is a rectangle if convex, and an "angular eight" with corners on a rectangle if non-convex." at http://www.google.ca/imgres?imgurl=http://www.scientific-web.com/en/Mathematics/Geometry/images/Quadrilateral2.png&imgrefurl=http://www.scientific-web.com/en/Mathematics/Geometry/Quadrilateral.html&h=546&w=439&sz=34&tbnid=aVnI35NJLQIezM:&tbnh=251&tbnw=202&prev=/images%3Fq%3Dequiangular%2Bquadrilateral&usg=__YqmeQj60_YmSg_s1DT2QVuqYjOA=&ei=MEzRS_OwKYXitgOW8PTFCQ&sa=X&oi=image_result&resnum=2&ct=image&ved=0CAYQ9QEwAQ

Do anyone have any sources for calling this a crossed rectangle - and wouldn't "regular bow-tie quadrilaterals" or "equiangular quadrilaterals" be a better name for this file?--JimWae (talk) 19:17, 23 April 2010 (UTC)


 * Mathworld Quadrilateral "crossed quadrilaterals (or butterflies, or bow-ties; right figure)." The terminology is also used in the intersecting antiprirms, like Pentagrammic_crossed-antiprism, which have "crossed quadrilateral" vertex figures. It looks like lots of references to "crossed quadrilaterals", like . It's only briefly given at Quadrilateral. There seems to be competing terminology, with complex polygon used in computer science, while confusing in mathematics with complex numbers and complex polytopes meaning something else. Tom Ruen (talk) 21:05, 23 April 2010 (UTC)
 * p.s. A Skew polygon would be nonplanar (twisted), and yes, that's something else. Tom Ruen (talk) 21:08, 23 April 2010 (UTC)

So nothing for "crossed-rectangle" nor "complex rectangle", correct?--JimWae (talk) 21:23, 23 April 2010 (UTC)


 * Nothing?! I figured a quadrilateral is a generalized 4-sided polygon, so the terminology would track back to specialized quads too. On a quick search, uniform polyhedra vertex figures reference the names: Tom Ruen (talk) 21:54, 23 April 2010 (UTC)
 * Vertex figures Crossed trapezoid, crossed rectangle
 * Uniform Polyhedra crossed trapezoid, crossed rectangle

I can only read the first & it does not appear to settle anything. Two questions then: 1>Is a crossed rectangle "still" a rectangle? 2>Does "crossed rectangle" mean a rectangle with the diagonals drawn in & sides remaining? or does it mean a (180 degree) twisted rectangle? JimWae (talk) 22:01, 23 April 2010 (UTC)

Looking closer at the 1st source, it does appear that the source intends twisted (though the other usage also exists, I think). Still no source I can find defines rectangle to include "crossed" ones.--JimWae (talk) 22:18, 23 April 2010 (UTC)


 * Crossed seems to be a widely used prefix qualifier for quadrilateral and polygon, so I have no comparable terms, except complex, again which seemes to be focused on computer graphics, rather than geometry.
 * And you are mistaken on the 1st source - ALL uniform polyhedra have planar polygons as vertex figures. That term is skew polygon in ALL such cases I've seen. Tom Ruen (talk) 23:08, 23 April 2010 (UTC)

My concern is whether the possible "existence" of "crossed-rectangles" affects the definition of rectangle. I do not see how discussion of 3 dimensional and non-planar figures enters into a discussion of rectangle--JimWae (talk) 18:31, 24 April 2010 (UTC)


 * I could see argument that it might be better to have a section under quadrilateral as more general. But non-planar figures are not being considered under crossed-rectangle. Tom Ruen (talk) 00:09, 25 April 2010 (UTC)

I was just trying to make sense of your 23:08 23 April 2010 comment above. Maybe you were referring to my use of "twisted" related to my saying rectangular wire frames could be twisted to form a bow-tie shape. My concern is only with planar figures -- & talk of polyhedra also seems off-topic to me. Incidentally, is there no disagreement about calling bow-ties quadrilaterals? I am sure some would say they have 6 sides. JimWae (talk) 00:32, 25 April 2010 (UTC)