Decomposing a cube into the sum of adjacent odd numbers is an
exercise in the book Introduction to Data Structures and
Algorithm Analysis by T. L. Naps, 2nd Edition, St. Paul, Minnesota:
West Publishing Co., 1992. On p. 50, prob. 4, the problem
is attributed to the book Introduction Arithmetica by Nicomachus,
written in the first century A.D. The Eight Cubes image
was composed by A. Klinger using the NeXTStep Diagram LightHouse
program to display reasoning toward its solution. Papers on this issue
appear as: Cubes
(in
collaboration with P. Stelling); and, Cubes,
Basics
(benefitting from discussions with R. Blattner, P. Stelling,
and B. Manel).
Loren McQuade took and digitized the Regular Solids images.
Mathematica created the "Tetra" images thanks to assistance and guidance from Eskandar Ensafi. A. Klinger calculated (x,y,z) locations of solid vertices used for both the "decahedr" images. The names given this solid include cuboctahedron, rhombic dodecahedron, dymaxion. I've called it a tetradecahedron, although that implies fourteen equal-area same-shape faces. References.
