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Topic: Classification of quadrilaterals
Replies: 17   Last Post: Jan 11, 1995 6:43 AM

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John Conway

Posts: 2,238
Registered: 12/3/04
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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