Regular cube surface tours
by Jan Kristian Haugland

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Other polyhedra:   Tetrahedron   Octahedron   Icosahedron

Here is a collection of (presumably) all regular cube 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. Next to the label, there is one or more illustration(s) (one for each (a, b) pair). These are also clickable for a better view of each one.

One might suspect that the number of vertices of a regular cube surface tour with two different (a, b) pairs and no double edges must be either 3 times a triangular number, or 8 times a generalized pentagonal number.

ToursIllustrationsCommentsAdditional illustrations
0 No crossing points

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

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

Same as Octahedron-4
and Icosahedron-4
8 Same as Icosahedron-8
9 Same as Octahedron-9C
and Icosahedron-9
12A
12B Contains double edges

Same as Octahedron-12B
and Icosahedron-12
16 Same as Icosahedron-16
18 Same as Octahedron-18A
and Icosahedron-18
20Same as Icosahedron-20
24A
24BSame as Icosahedron-24B
24C Contains double edges

Same as Octahedron-24B
and Icosahedron-24C
28
30 Same as Octahedron-30C
and Icosahedron-30
32
36A
36BSame as Icosahedron-36
40A
40B Contains double edges

Same as Octahedron-40B
and Icosahedron-40B
44A
44BSame as Icosahedron-44
44C
45A Same as Octahedron-45C
and Icosahedron-45B
45BSame as Icosahedron-45A
48A
48B
56A
56B
56CSame as Icosahedron-56A
60A
60B Contains double edges

Same as Octahedron-60C
and Icosahedron-60
63A
63B Same as Octahedron-63C
and Icosahedron-63C
63CSame as Icosahedron-63B
66
68ASame as Icosahedron-68A
68BSame as Icosahedron-68B
69
72A
72B
72C
80A
80B
80C
84A Same as Octahedron-84A
and Icosahedron-84A
84B
84C Contains double edges

Same as Octahedron-84F
and Icosahedron-84B
88A
88B
93
96A
96B
96C
96DSame as Icosahedron-96B
96E
100A
100B
104A
104B
108A Same as Octahedron-108C
and Icosahedron-108A
108BSame as Icosahedron-108B
108C
108DSame as Icosahedron-108C
112A
112B Contains double edges

Same as Octahedron-112B
and Icosahedron-112B
114
116
120A
120B
120C
120D
126
128A
128B
128C
128DSame as Icosahedron-128
129
135A Same as Octahedron-135G
and Icosahedron-135B
135BSame as Icosahedron-135C
135CSame as Icosahedron-135A
136
144A
144B
144CSame as Icosahedron-144B
144D Contains double edges

Same as Octahedron-144E
and Icosahedron-144C
148
150A
150B
152A
152B
156A
156B
156C
164ASame as Icosahedron-164A
164BSame as Icosahedron-164B
165A Same as Octahedron-165A
and Icosahedron-165D
165BSame as Icosahedron-165C
168
171A
171B
174
176A
176B
176C
180 Contains double edges

Same as Octahedron-180E
and Icosahedron-180
184A
184B
184CSame as Icosahedron-184
192
195
196
198A Same as Octahedron-198G
and Icosahedron-198B
198BSame as Icosahedron-198A
200A
200B
200C
200DSame as Icosahedron-200