A construction of magic 24-cells

I found a novel class of magic square analogue, magic 24-cell. The problem is to assign the consecutive numbers 1 through 24 to the vertices in a graph, which is composed of 24 octahedra and 24 vertices, to make the sum of the numbers of each octahedron the same. It is known that there are facet-magic and face-magic labelings of tesseract. However, because of 24-cell contains triangle, face-magic labeling to assign different labels to each vertex is impossible. So I tried to make a cell-magic labeling of 24-cell. Linear combination of three binary labeling and one ternary labeling gives 64 different magic labelings of 24-cell. Due to similarity in the number of vertices between 5x5 magic square and magic 24-cell, It might be possible to calculate the number of magic 24-cell. Further analysis would be need to determine the number of magic 24-cell.Comment: My implementation is available on Github. https://github.com/gwahak/mathematic

Range of magic constant on Hexagonal Tortoise Problem

Hexagonal tortoise problem (HTP), also known as Jisuguimundo or Jisugwimundo, is a magic square variety which was invented by medieval Korean Mathematician and minister Suk-Jung Choi (1646-1715).[1] Choi showed pattern 30 vertices 3 by 3 diagonal shape which has 93 as its magic constant. Unlike magic square, vertices in Jisugwimundo counted one times, twice or three times. This change makes magic constant of Hexagonal Tortoise Problem could be vary. We consider a range of hexagonal sums in various Jisugwimundo. In this paper, we decomposed vertices on Jisugwimundo to some groups. by this way we found the range of magic constant on several HTP.Comment: 16 page

A Hybrid Genetic Algorithm for the Hexagonal Tortoise Problem

Abstract. We propose a hybrid genetic algorithm for the hexagonal tortoise problem. We combined the genetic algorithm with an efficient local heuristic and aging mechanism. Another search heuristic which focuses on the space around existing solutions is also incorporated into the genetic algorithm. With the proposed algorithm, we could find the optimal solutions of up to a fairly large problem.