Wikimedia Commons

Category:Paths in hypercubes (blue alt)

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Square Cube Tesseract Step from dimension n to n+1
Petrie
polygon
  • keep first half of old path
  • move second half to next dimension
(adding 2n to each vertex index)
  • connect ends with two new edges (orange)

Old number of edges:   2n
New number of edges:   2n + 2   =   2(n+1)

first half of path = Sloane's A000225(0..n)

Gray
code
path
  • keep old path without closing edge
  • duplicate it in new dimension
(adding 2n to each vertex index)
  • connect ends with two new edges (orange)

Old number of edges:   2n
New number of edges:   2(2n−1) + 2   =   2n+1

path = Sloane's A003188(0..2n−1)

Note that the 1-cube has a single edge, while both its Petrie polygon and its Gray code path are the corresponding digon with two edges.

Media in category "Paths in hypercubes (blue alt)"

The following 5 files are in this category, out of 5 total.

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