<ul data-eligibleForWebStory="true"><li>63 is a centered octahedral number, representing the number of cubes in an octahedron when built using a specific pattern.</li><li>René Just Haüy developed a crystal formation theory in the late 1700s, involving orderly arrangements of cubes to form an octahedron.</li><li>The sequence revealing numbers similar to 63 and less than 10,000 includes 129, 231, 377, 575, 833, 1159, 1561, 2047, 2625, 3303, 4089, 4991, 6017, 7175, 8473, and 9919.</li><li>63 is also a significant number in Delannoy numbers, indicating the ways to traverse a grid using specific directions.</li><li>There are 63 possible movements on a 3x3 grid following the rules.</li><li>In a Haüy octahedron with N layers, the number of cubes is equal to the number of Delannoy steps on a 3xN grid.</li><li>Further exploration is desired to establish a geometric explanation for the similarity between Haüy octahedron and Delannoy grids.</li><li>Claude assisted in creating octahedron diagrams using a Python program, highlighting the benefits of casual hobby programming with AI help.</li></ul>

Ned Batchelder: Math factoid of the day: 63

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