Re: Orange stacks

In article <1052vlk$3dn0r$1@dont-email.me>,
David Entwistle  <qnivq.ragjvfgyr@ogvagrearg.pbz> wrote:

Then one shape (from the square pyramid) has a square top and bottom. It
looks to me like a truncated octahedron.

Top layer:

  .       .       .
 
      a       b

  .       .        .

      c       d

  .       .        .


Middle layer:

  e       f       g

      .        .

  h       i       j

      .        .

  k       l       m


Bottom layer:

  .       .       .

      n       o

  .       .        .

      p       q

  .       .        .

If you consider the octahedron based on the square f, h, j, and l,
then the balls on the top and bottom layers do not fall on its faces -
in fact they are directly above and below the edges of the square: a
is directly above the midpoint of hf and n below it, forming a square
face.

There are in fact 6 square faces: abcd, nopq, ahnf, bfoj, djql, and
clph.  And 8 triangular faces: abf, bdj, dcl, cah, nof, oqj, qpl, and
pnh.  This is a cuboctahedron.

The second shape (from the triangular pyramid) is based exclusively on
equilateral triangles and is entirely regular [...]

I can see I'm going to have to buy some golf balls, or table tennis balls.

You will find that the second shape is also not what you think it is.

-- Richard