The Grand Army Puzzle
Circa late 1800's?
(7/8 by 7/8 by 2.1 inch box with three identical 5/8" wood cubes;
original label on top was lost and replaced by a copy from an identical puzzle)
The Grand Army Of the Republic
was a veterans organization formed after the American civil war
(see the Wikipedia page).
This puzzle has three identical cubes,
each colored red, white, and blue
on three pairs of adjacent faces.
Like the four cube
the object is to arrange the three cubes in a line so that each side has no duplicate colors.
Below is a solution and its graph
(constructed as for Instant Insanity);
it is unique up to repositioning the puzzle and reordering the cubes
(e.g., replacing cycle 2 by R - 3 - W - 1 - B - 2 - R is the same as rotating 180 degrees,
rotating forward 90 degrees,
and exchanging cubes 1 and 2):
cycle 1: R - 1 - W - 2 - B - 3 - R
cycle 2: R - 2 - W - 3 - B - 1 - R