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Replies: 17   Last Post: Jan 11, 1995 6:43 AM

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 John Conway Posts: 2,238 Registered: 12/3/04
Posted: Dec 18, 1994 4:02 PM

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

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.

Date Subject Author
12/15/94 E7M2WAT@TOE.TOWSON.EDU
12/16/94 W Gary Martin
12/16/94 Henri Picciotto
12/17/94 John Conway
12/17/94 roitman@oberon.math.ukans.edu
12/18/94 John Conway
12/20/94 Chenteh Kenneth Fan
12/21/94 John Conway
12/21/94 Walter Whiteley
12/21/94 William T. Webber
12/21/94 James King
12/21/94 Chenteh Kenneth Fan
12/21/94 John Conway
12/21/94 John Conway
12/21/94 John Conway
12/21/94 Chenteh Kenneth Fan
12/21/94 Chenteh Kenneth Fan
1/11/95 joe malkevitch