I got my "Speculations on the Fourth Dimension, Selected Writings of
Charles H. Hinton", Dover, 1980, back. It doesn't reprint Hinton's
description of his cubes, but Rudolf v.B.Rucker, in the introduction
describes something more of them:
"The second part of "A New Era of Thought" consists of a description
of how to visualize a tesseract by looking at various 3-D cross sections
of it. On is to construct a set of 12 cubes, coloring the faces, edges
and corners all manner of different colors. (Eighty-one different colors
are used, and some rather unfamiliar ones are resorted to. ...)Eight of
these cubes make up the boundaries of the hypercube, and the four others
are cross sections taken between pairs of opposite cubes. The way in
which all the cubes fit together is really explained rather well, if one
has the will to endure not only 81 colors, but the 81 Latin names which
Hinton assigns to the parts of the tesseract.
"In addition to the set of 12 large cubes, there was also to be a set of 81
small monochrome cubes, each representing a part of the tesseract. By
moving theese little cubes about one could better comprehend the fact that
rotation through the fourth dimension corresponds to mirror image reflection
in 3-D space."
In Hinton's book "The Fourth Dimension", published n 1904, he has a
streamlined version of the tesseract section models. "There were actually
three parts to the complete set of tesseract models. There was a set of 27
"slabs," actually cardboard squares; a set of 81 one-inch monochrome cubes,
each a different color; and a set of 12 multicolored "catalogue cubes,"
which were depicted in a color plate bound into "The Fourth Dimension". When
the book came out, one could buy a set consisting of the 27 slabs and the
81 little cubes for 16 shillings, or a set consisting of the 12 catalogue
cubes for 21 shillings."
If anyone on this list can find a copy of "The Fourth Dimension", I, for
one, would like to buy it. I wonder if any of the models are around anywhere?