Re: Orange stacks

In article <10527u5$391km$1@dont-email.me>,
David Entwistle  <qnivq.ragjvfgyr@ogvagrearg.pbz> wrote:

If each orange (same size sphere) is packed so it touches 12 others,
then the packing density is the same for the stackings you mentioned.

It's not merely that the density is the same.

Thanks. If I draw the layers out, I can see that.
>
Square base: 1, 4, 9, 16 in each layer. If I take the middle of the nine
as my reference, it touches (from the top) 0, 4, 4, 4 = 12.
>
Triangular base: 1, 3, 6, 10, 15 in each layer. If I take the middle of
the ten as my reference, it touches (from top) 0, 0, 3, 6, 3 = 12.
>
If I have this right, if I build my pyramids and glue the twelve touching
elements to the reference element, making two shapes, both of thirteen
elements each,

Yes.

then I finish up with two quite different shapes with quite
different symmetries.

But - hard though it may seem to believe - no!

-- Richard