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).

Answer: CANCRINITE