diamonds, bliamonds

Paul E. wrote...

>Since diamonds don't tesselate to fill ratio space, this use of the word
>seems quite incorrect.

I don't know about the use of the word, but 2-d diamonds do fill ratio
space when represented on a triangular lattice. In a sense, so do 3-d
ones; even tho there are octahedral holes, they contain no uncovered
lattice points. Would this be considered a semi-regular 3-d tiling
(whereas the 2d diamond tiling is regular)? I'm not sure about higher
dimensions... my intuition is that this holds (for example, a local group
of 6-factor diamonds does seem to grab all the notes in the Eikosany).

-Sea.

Carl Lumma wrote,

>Paul E. wrote...

>>Since diamonds don't tesselate to fill ratio space, this use of the word
>>seems quite incorrect.

>I don't know about the use of the word, but 2-d diamonds do fill ratio
>space when represented on a triangular lattice. In a sense, so do 3-d
>ones; even tho there are octahedral holes, they contain no uncovered
>lattice points. Would this be considered a semi-regular 3-d tiling
>(whereas the 2d diamond tiling is regular)? I'm not sure about higher
>dimensions... my intuition is that this holds (for example, a local group
>of 6-factor diamonds does seem to grab all the notes in the Eikosany).

In any case, the relevant point is not whether they fill ratio space, but
whether they fill ratio space with only unison vectors mapping one diamond
to a neigboring one. Sorry I didn't express this fully. For those joining us
now, "the word" I was referring to above was finity, since Joe Monzo started
using the word to describe the size of the diamonds.

>-Sea.

Ocean?