Regular cube surface tours

by
Jan Kristian Haugland

Back to Regular polyhedron surface tours main page

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.

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 |