
Re: Classification of quadrilaterals
Posted:
Dec 18, 1994 4:02 PM


I think I've found some very nice names for the symmetry types of polygons, namely
mreflexive means "having just m reflections, but not:"
mlateral, which means that all the reflections are lateral, or
mdiagonal, which means that they are all diagonal. Finally
mchiral means "having no reflections, but just m rotations".
A reflection is lateral if it swaps two opposite edges, diagonal if it swaps two opposite vertices.
For triangles:
3reflexive = equilateral
1reflexive = isosceles
1chiral = scalene
For quadrilaterals
4reflexive = square
2lateral = rectangle
2diagonal = rhombus
2chiral = parallelogram
1lateral = isosceles trapezium
1diagonal = kite
1chiral = totally irregular.
I would in fact use the Latinbased prefixes, thus
"bilateral, unidiagonal, etc."
For hexagons, the types are
6reflexive = regular
trilateral, tridiagonal, trichiral
bireflexive, bichiral
unilateral, unidiagonal, unichiral
I see that "chiral", which means "handed", is Greek, so doesn't really go with these Latin prefixes. So I think I'll change it to "rotational".
John Conway.

