Regular cube surface tours
by
Jan Kristian Haugland
Back to Regular polyhedron surface tours main page
Other polyhedra: Tetrahedron Octahedron Dodecahedron 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.
Tours | Illustrations | Comments | Additional illustrations | |||
0 | No crossing
points Same as Octahedron-0 and Icosahedron-0 | |||||
3 | Contains 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 | |||||
20 | Same as Icosahedron-20 | |||||
24A | ||||||
24B | Same 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 | ||||||
36B | Same as Icosahedron-36 | |||||
40A | ||||||
40B | Contains double edges Same as Octahedron-40B and Icosahedron-40B | |||||
44A | ||||||
44B | Same as Icosahedron-44 | |||||
44C | ||||||
45A | Same as Octahedron-45C and Icosahedron-45B | |||||
45B | Same as Icosahedron-45A | |||||
48A | ||||||
48B | ||||||
56A | ||||||
56B | ||||||
56C | Same as Icosahedron-56A | |||||
60A | ||||||
60B | Contains double edges Same as Octahedron-60C and Icosahedron-60 | |||||
63A | ||||||
63B | Same as Octahedron-63C and Icosahedron-63C | |||||
63C | Same as Icosahedron-63B | |||||
66 | ||||||
68A | Same as Icosahedron-68A | |||||
68B | Same 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 | ||||||
96D | Same as Icosahedron-96B | |||||
96E | ||||||
100A | ||||||
100B | ||||||
104A | ||||||
104B | ||||||
108A | Same as Octahedron-108C and Icosahedron-108A | |||||
108B | Same as Icosahedron-108B | |||||
108C | ||||||
108D | Same 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 | ||||||
128D | Same as Icosahedron-128 | |||||
129 | ||||||
135A | Same as Octahedron-135G and Icosahedron-135B | |||||
135B | Same as Icosahedron-135C | |||||
135C | Same as Icosahedron-135A | |||||
136 | ||||||
144A | ||||||
144B | ||||||
144C | Same as Icosahedron-144B | |||||
144D | Contains double edges Same as Octahedron-144E and Icosahedron-144C | |||||
148 | ||||||
150A | ||||||
150B | ||||||
152A | ||||||
152B | ||||||
156A | ||||||
156B | ||||||
156C | ||||||
164A | Same as Icosahedron-164A | |||||
164B | Same as Icosahedron-164B | |||||
165A | Same as Octahedron-165A and Icosahedron-165D | |||||
165B | Same as Icosahedron-165C | |||||
168 | ||||||
171A | ||||||
171B | ||||||
174 | ||||||
176A | ||||||
176B | ||||||
176C | ||||||
180 | Contains double edges Same as Octahedron-180E and Icosahedron-180 | |||||
184A | ||||||
184B | ||||||
184C | Same as Icosahedron-184 | |||||
192 | ||||||
195 | ||||||
196 | ||||||
198A | Same as Octahedron-198G and Icosahedron-198B | |||||
198B | Same as Icosahedron-198A | |||||
200A | ||||||
200B | ||||||
200C | ||||||
200D | Same as Icosahedron-200 |