All of my documents summarized in the following table have been referred
to elsewhere on this website but are brought together here as a single list. All are
available for download. The common feature among all these documents is that cubes of
all sizes are treated as belonging to a family. In that regard mathematical properties
usually need to be and are expressed as functions of cube size. Where applicable, cube
solving algorithms are also shown as functions of cube size.
| Title |
Filename |
Size kb |
Comment |
| Rubik's Cube Extended: Derivation of Number of States for Cubes of
Any Size and Values for up to Size 25x25x25 |
cubestates.pdf |
192 |
Mathematical document that derives the number of reachable states for
cubes of all sizes. Based on original 1991 document. Can be reproduced using a monochrome printer. |
| Calculations for Extended Rubik's Cube |
cubecalc.xls |
120 |
Performs numerical calculations and chart plotting primarily for cubes
with standard (unmarked) centres referred to in cubestates.pdf. |
| Calculations for Extended Rubik's Cube with Marked Centres |
cubecalc_mark.xls |
116 |
Performs numerical calculations and chart plotting for cubes with marked
centres referred to in cubestates.pdf. |
| Rules for Rubik's Family Cubes of All Sizes |
cuberules.pdf |
183 |
Mathematical document that has particular emphasis on parity and unreachable
states. Makes use of results from cubestates.pdf. |
| Instructions for Solving Rubik Family Cubes of Any Size |
cubesolving.pdf |
333 |
Includes very little mathematics. Uses move notation that corresponds to
that used for my Unravel software but algorithms can be applied to any other hardware or software
implementations. |
| Implementing and Solving Rubik's Family Cubes with Marked Centres |
markctr.pdf |
1218 |
Covers implementation design techniques used in the Java Unravel program
for cubes with marked centres. Provides details of additional algorithms, relative to those for solving
standard cubes, which are required for solving cubes with marked centres. |
| Rubik's n x n x n Cube Family |
cubereview.htm
cubereview.zip |
82 |
Attempts to review the status of Rubik's family cubes around the year 2010
with particular emphasis on cubes of large size. Zip version includes images making it convenient for download. |