Ahuitzotl's Art Gallery

David McIlroy, Liz Demicco

HINTS:

- Have you looked closely at the items to see how they're similar? Can you turn them around?
- The sacrifices are important later.
- These are just one cell; imagine if they were tiled in 3 dimensions.

SOLUTION:

All of these items have been constructed with very specific symmetries.

They are:

Gloves - Orthorhombic, symmetry Pca2_1 (space group #29)

Fruit - Orthorhombic, symmetry Pmmm (space group #47)

Arms - Tetrahedral, symmetry P4/m (space group #83)

Fish - Tetrahedral, symmetry P4_2/nmc (space group #137)

Glasses - Hexagonal, symmetry P6/mmm (space group #191)

Algebra - Cubic, symmetry Fd-3m (space group #227)

All of the space groups in this set are prime numbers whose digits sum to 11. ("eleven captive warriors in the prime of their manhood")

There's one missing, though--#173, which is Hexagonal, symmetry P6_3.

The solvers have to make this for us. When they do, we give them the word CANCRINITE (which has symmetry P6_3).