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Magic hexagram

Wikipedia contributorsAdapted for Fathomly · View authors
1 min read
Source updated July 29, 2025
Image credit is listed at the end of this article.

A magic hexagram of order 2 is an arrangement of numbers in a hexagram with triangular cells with 2 cells on each edge, in such a way that the numbers in each row, in all three directions, sum to the same magic constant M.

01Magic star hexagram

Magic star hexagram or 6-pointed magic star is a star polygon with Schläfli symbol {6/2} in which numbers are placed at each of the six vertices and six intersections, such that the four numbers on each line sum to the same magic constant.

02Magic star hexagram with triangular cell

There are two solutions of magic star hexagram with 12 triangular cells.

03Magic star hexagram with more than 12 vertices

Harold Reiter and David Ritchie calculated the solution of magic hexagrams with 19 vertices.

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Sources and credits

This article is adapted from the Wikipedia article “Magic hexagram”, written by its contributors and licensed under CC BY-SA 4.0. Fathomly has changed the layout, removed citation markers, navigation and maintenance notices, and adjusted punctuation. This adapted version is shared under the same license. For references, see the original article.

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Related topics

Magic square

In mathematics, especially historical and recreational mathematics, a magic square is a square array of numbers, usually positive integers, where the sums of the numbers in each row, each column, and both main diagonals are the same. The order of a magic square is the number of integers along one side, and the constant sum is called the magic constant or magic sum.

Magic hexagon

A magic hexagon of order n is an arrangement of numbers in a centered hexagonal pattern with n cells on each edge, in such a way that the numbers in each row, in all three directions, sum to the same magic constant M. A normal magic hexagon contains the consecutive integers from 1 to 3n2 − 3n + 1. Normal magic hexagons exist only for n = 1 and n = 3.