Regular octahedron surface tours
by Jan Kristian Haugland

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Other polyhedra:   Tetrahedron   Cube   Icosahedron

Here is a collection of (presumably) all regular octahedron surface tours with at most 200 vertices. Each one is given a label according to the
number of vertices. The label links to a text file containing the tour presented like a Gauss code for knots, except that we are not specifying
"over" and "under" crossings, and it also contains the feasible values of a and b. No extra letters means that the particle moves midways between
parallel grid lines. "s" or "ss" after (a, b) means it is skewed to one side to some degree: an "s" tour goes through the centre of every other grid
triangle; an "ss" tour passes the centres on the same side. An "x" in the label indicates that the graph contains at least one vertex of degree 6. Next
to the label, there is one or more illustration(s) (one for each (a, b) pair, or skewed variant). These are also clickable for a better view of each one.

ToursIllustrationsCommentsAdditional illustrations
0 No crossing points

Same as Cube-0
and Icosahedron-0
3Contains double edges

Same as Cube-3
and Icosahedron-3
4Contains double edges

Same as Cube-4
and Icosahedron-4
7xContains double edges
9AContains double edges
9BContains double edges
9CSame as Cube-9
and Icosahedron-9
12AContains double edges
12BContains double edges

Same as Cube-12B
and Icosahedron-12
16x
18A Same as Cube-18
and Icosahedron-18
18B
24AContains double edges
24BContains double edges

Same as Cube-24C
and Icosahedron-24C
24xContains double edges
30AContains double edges
30BContains double edges
30CSame as Cube-30
and Icosahedron-30
30xContains double edges
36AContains double edges
36BContains double edges
39xA
39xB
40AContains double edges
40BContains double edges

Same as Cube-40B
and Icosahedron-40B
45A
45B
45CSame as Cube-45A
and Icosahedron-45B
45D
45E
46x
48Contains double edges
51xContains double edges
54A
54B
57x
60AContains double edges
60BContains double edges
60CContains double edges

Same as Cube-60B
and Icosahedron-60
60x
63AContains double edges
63BContains double edges
63CSame as Cube-63B
and Icosahedron-63C
63D
63E
67xContains double edges
72A
72B
72CContains double edges
72x
81AContains double edges
81BContains double edges
81xContains double edges
84ASame as Cube-84A
and Icosahedron-84A
84B
84C
84DContains double edges
84EContains double edges
84FContains double edges

Same as Cube-84C
and Icosahedron-84B
84xContains double edges
87x
88xContains double edges
94x
96Contains double edges
99AContains double edges
99BContains double edges
99C
99D
102AContains double edges
102BContains double edges
108A
108B
108CSame as Cube-108A
and Icosahedron-108A
108DContains double edges
108EContains double edges
108FContains double edges
111xContains double edges
112AContains double edges
112BContains double edges

Same as Cube-112B
and Icosahedron-112B
115x
117x
120xContains double edges
121x
132AContains double edges
132BContains double edges
135AContains double edges
135BContains double edges
135C
135D
135E
135F
135GSame as Cube-135A
and Icosahedron-135B
135H
135I
135xContains double edges
136Contains double edges
136xContains double edges
138x
144AContains double edges
144BContains double edges
144CContains double edges
144DContains double edges
144EContains double edges

Same as Cube-144D
and Icosahedron-144C
147xA
147xB
153xContains double edges
160x
162AContains double edges
162BContains double edges
162C
162D
165ASame as Cube-165A
and Icosahedron-165D
165BContains double edges
165CContains double edges
165D
165E
168xA
168xB
168xC
171A
171B
174x
180AContains double edges
180BContains double edges
180CContains double edges
180DContains double edges
180EContains double edges

Same as Cube-180
and Icosahedron-180
183AContains double edges
183BContains double edges
187xContains double edges
189x
192A
192B
192CContains double edges
192xContains double edges
198A
198B
198C
198D
198E
198F
198GSame as Cube-198A
and Icosahedron-198B
198H
198I