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Re: Classification of quadrilaterals
Posted:
Dec 18, 1994 4:02 PM
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I think I've found some very nice names for the symmetry types
of polygons, namely
m-reflexive means "having just m reflections, but not:"
m-lateral, which means that all the reflections are lateral, or
m-diagonal, which means that they are all diagonal. Finally
m-chiral 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:
3-reflexive = equilateral
1-reflexive = isosceles
1-chiral = scalene
For quadrilaterals
4-reflexive = square
2-lateral = rectangle
2-diagonal = rhombus
2-chiral = parallelogram
1-lateral = isosceles trapezium
1-diagonal = kite
1-chiral = totally irregular.
I would in fact use the Latin-based prefixes, thus
"bilateral, unidiagonal, etc."
For hexagons, the types are
6-reflexive = 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.
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