Tesseract Magick I Of Iii

Tesseract Magick [Part I of III] The concept of Tesseract Magick was originally developed and promulgated by Ebony Anpu and continued by various groups and individuals since his death. A tesseract is what is referred to as a 4-cube or hypercube, loosely defined as a fourth-dimensional equivalent to a standard cube. A threedimensional cube has (8) vertices, (8) edges and (6) faces. By comparison, a tesseract has (16) vertices, (32) edges, (24) faces and in fact can be “unrolled” into (8) cubes the same way a standard cube can “unroll” into a cavalry cross. Let us consider how a tesseract is constructed. For convenience, the (16) vertices of the tesseract have been labeled from 0 to 15. If you look at the bottom of the image you can easily locate point 0, and a quick examination will reveal that vertex 0 connects to points 1, 2 and 3 to form a face. However, the layout of a tesseract can be very difficult to follow, and people unfamiliar with the intricate layout of this figure may have trouble. Luckily, there exists a simple chart that can reveal the construction of a tesseract and more importantly the relation of those components to the other portions of the tesseract.

© Michael A. Eckhard, 2009. Permission is freely granted to distribute this work so long as the document is left unaltered.

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Tesseract Magick [Part I of III] The figure below is referred to mathematically as an adjacency matrix, which I will refer to as the base table for convenience. The base table can show one how to verify all faces and even cubes in the tesseract and their relationships to each other. Let us now learn about the relationships that can be discovered using this table. Using the base table, it is easy to identify all of the 24 faces of the tesseract. All rows and columns reflect a face, so for example vertices 5,4,12 and 13 form a face and vertices 5,7,3 and 1 form a face as well. Please take a moment to review on the tesseract drawing to verify you understand. Now that you have verified the vertices of 8 faces, we can discover the others. On the base table, a 2x2 grouping of squares is also a face, so for example vertices 8,9,10 and 11 form a face as does 10,2,6 and 14. Note that as you move from right to left, these faces “wrap around” back to the other side. For example, the square labeled 5 in the top right wraps around to 1,9 and 13 to form a square. For your convenience I have shown small squares to help illustrate this for you, inserting more “phantom base squares” to aid in understanding. With the (16) additional faces now shown, we can now identify all faces on a tesseract.

© Michael A. Eckhard, 2009. Permission is freely granted to distribute this work so long as the document is left unaltered.

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Tesseract Magick [Part I of III] To find the eight cubes within a tesseract the method is even simpler. Every 2x4 grid of squares are the vertices of a particular cube. The image below shows them in two colors for easy reference. It should be understood that it is also possible to determine all vertices that connect to any given vertex. In this case, taking the north, south, east and west neighbors will show these relationships. For example, vertices 14,2,8 and 11 are directly connected to vertex number 10. Again, please verify of the tesseract illustration to verify this.

© Michael A. Eckhard, 2009. Permission is freely granted to distribute this work so long as the document is left unaltered.

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