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His interest in magic squares led to higher dimensions: magic cubes, tesseracts, etc. He developed a new diagram for the four-dimensional tesseract. This was published in 1962 when he showed constructions of four-, five-, and six-dimensional magic hypercubes of order three. [1] He later was the first to publish diagrams of all 58 magic ...
Mechanically identical to the standard 3×3×3 cube, but with specially printed stickers for displaying the date. Much easier to solve since five of the six faces are ignored. Ideal produced a commercial version during the initial cube craze. Sticker sets are also available for converting a normal cube into a calendar. Commercial Name: Magic Cube
It contains no magic squares. The smallest pantriagonal magic cube has order 4. A pantriagonal magic cube is the 3-dimensional equivalent of the pandiagonal magic square – instead of the ability to move a line from one edge to the opposite edge of the square with it remaining magic, you can move a plane from one edge to the other.
For the diagonal or pandiagonal classes, one or possibly 2 of the 6 oblique magic squares may be pandiagonal magic. All but 6 of the oblique squares are 'broken'. This is analogous to the broken diagonals in a pandiagonal magic square. i.e. Broken diagonals are 1-D in a 2-D square; broken oblique squares are 2-D in a 3-D cube.
For example the following sequence can be used to form an order 3 magic square according to the Siamese method (9 boxes): 5, 10, 15, 20, 25, 30, 35, 40, 45 (the magic sum gives 75, for all rows, columns and diagonals). The magic sum in these cases will be the sum of the arithmetic progression used divided by the order of the magic square.
An example of a 3 × 3 × 3 magic cube. In this example, no slice is a magic square. In this case, the cube is classed as a simple magic cube.. In mathematics, a magic cube is the 3-dimensional equivalent of a magic square, that is, a collection of integers arranged in an n × n × n pattern such that the sums of the numbers on each row, on each column, on each pillar and on each of the four ...
A geometric magic square, often abbreviated to geomagic square, is a generalization of magic squares invented by Lee Sallows in 2001. [1] A traditional magic square is a square array of numbers (almost always positive integers ) whose sum taken in any row, any column, or in either diagonal is the same target number .
Three-dimensional tic-tac-toe on a 3×3×3 board. In this game, the first player has an easy win by playing in the centre if two people are playing. One can play on a board of 4x4 squares, winning in several ways. Winning can include: four in a straight line, four in a diagonal line, four in a diamond, or four to make a square.