Building a Mystery

by Nathan Fung, with graphics by Joseph DeVincentis

ANSWER: REYNOLDS

 

The shapes provided can be assembled into a truncated cuboctahedron so that edge descriptions, where provided, are adjacent to a face with a letter that satisfied that description. However, this can only by accomplished by turning some of the faces so that they face the opposite direction inwards or outwards relative to the other faces (as clued in the flavor text).

There are two equivalent ways of assembling the solid (one is the inside out equivalent of the other) and one ring of 8 faces is turned opposite to all the other faces. These 8 faces in order spell the answer, REYNOLDS.