My Cube Publications

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

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.