by Polyhedron Dude » Sun Mar 16, 2014 9:07 am
Here are some leg patterns and possible walk patterns for 3 to 5 dimensional "humans".
Three-Dimensional
Dyadic leg pattern - that's us, 2 legs at the vertices of a dyad, we put one foot in front of the other - foot A then foot B, foot A, B, etc.
Four-Dimensional
Triangular leg pattern - this tetronian has trigonal symmetry and therefore three legs, his walk pattern will likely be in this pattern: A,B,C,A,B,C,A,B,C,...
Square leg pattern - this tetronian has either rectangular or square symmetry. He could have the following walk patterns: cyclic 4, bowtie, rectangular, or rhombic. Let A,B,C,D represent the four legs, where AB, BC, CD, and DA forms the lines of a square. Cyclic 4 would have this pattern A, B, C, D, A, B, C, D. Bowtie would go like A, B, D, C, A, B, D, C. Rectangular would move two legs at a time: AB, CD, AB, CD. Rhombic would move opposite legs at the same time: AC, BD, AC, BD. Rectangular and rhombic are the most likely walking methods for a square tetronian.
Pentagonal leg Pattern - This tetronian has pentagonal symmetry and has 5 legs. Possible walking patterns could be cyclic 5, cyclic 5/2, and "three-two". Cyclic 5 would have a A,B,C,D,E pattern and 5/2 would have a A,C,E,B,D pattern. Various "three-two" patterns would work - here's one: ABD, CE, ABD, CE.
Hexagonal leg pattern - This tetronian most likely has trigonal symmetry, but could have hexagonal. Most likely walking patterns would be the star-of-David walk and the "asterisk" walk. The star of David would go like this: ACE, BDF, ACE, BDF. The asterisk walk would go: AD, BE, CF, AD, BE, CF.
Five-Dimensional
Tetrahedral leg pattern - this pentonian has tetrahedral symmetry with four legs and would likely walk with a "disphenoid" walk - AB, CD, AB, CD
Octahedral leg pattern - this dude has either tetrahedral or octahedral symmetry with 6 legs arranged like the vertices of an octahedron. He would likely walk with a trigon antiprism pattern.
Cube leg pattern - this dude has 8 legs arranged like a cube, he may either walk in a square prism pattern or a stella octangula pattern - both moving four legs at a time.
Icosahedral leg pattern - has 12 legs. Most likely walk pattern may move four legs at a time, where these four legs form a golden rectangle going through the center of the ike.
Dodecahedral leg pattern - has 20 legs (this may be a bit overkill on number of legs needed, so may not get chosen as a 5-D human design). He would likely move 4 legs at a time, each four legs forming a tetrahedron in a 5-tet compound.
Whale Kumtu Dedge Ungol.