Regular octahedron surface tours

by
Jan Kristian Haugland

Back to Regular polyhedron surface tours main page

Other polyhedra: Tetrahedron Cube Dodecahedron 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.

Tours | Illustrations | Comments | Additional illustrations | |||

0 | No crossing points Same as Cube-0 and Icosahedron-0 | |||||

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

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

7x | Contains double edges | |||||

9A | Contains double edges | |||||

9B | Contains double edges | |||||

9C | Same as Cube-9 and Icosahedron-9 | |||||

12A | Contains double edges | |||||

12B | Contains
double edges Same as Cube-12B and Icosahedron-12 | |||||

16x | ||||||

18A | Same as Cube-18 and Icosahedron-18 | |||||

18B | ||||||

24A | Contains double edges | |||||

24B | Contains
double edges Same as Cube-24C and Icosahedron-24C | |||||

24x | Contains double edges | |||||

30A | Contains double edges | |||||

30B | Contains double edges | |||||

30C | Same as Cube-30 and Icosahedron-30 | |||||

30x | Contains double edges | |||||

36A | Contains double edges | |||||

36B | Contains double edges | |||||

39xA | ||||||

39xB | ||||||

40A | Contains double edges | |||||

40B | Contains
double edges Same as Cube-40B and Icosahedron-40B | |||||

45A | ||||||

45B | ||||||

45C | Same as Cube-45A and Icosahedron-45B | |||||

45D | ||||||

45E | ||||||

46x | ||||||

48 | Contains double edges | |||||

51x | Contains double edges | |||||

54A | ||||||

54B | ||||||

57x | ||||||

60A | Contains double edges | |||||

60B | Contains double edges | |||||

60C | Contains
double edges Same as Cube-60B and Icosahedron-60 | |||||

60x | ||||||

63A | Contains double edges | |||||

63B | Contains double edges | |||||

63C | Same as Cube-63B and Icosahedron-63C | |||||

63D | ||||||

63E | ||||||

67x | Contains double edges | |||||

72A | ||||||

72B | ||||||

72C | Contains double edges | |||||

72x | ||||||

81A | Contains double edges | |||||

81B | Contains double edges | |||||

81x | Contains double edges | |||||

84A | Same as Cube-84A and Icosahedron-84A | |||||

84B | ||||||

84C | ||||||

84D | Contains double edges | |||||

84E | Contains double edges | |||||

84F | Contains
double edges Same as Cube-84C and Icosahedron-84B | |||||

84x | Contains double edges | |||||

87x | ||||||

88x | Contains double edges | |||||

94x | ||||||

96 | Contains double edges | |||||

99A | Contains double edges | |||||

99B | Contains double edges | |||||

99C | ||||||

99D | ||||||

102A | Contains double edges | |||||

102B | Contains double edges | |||||

108A | ||||||

108B | ||||||

108C | Same as Cube-108A and Icosahedron-108A | |||||

108D | Contains double edges | |||||

108E | Contains double edges | |||||

108F | Contains double edges | |||||

111x | Contains double edges | |||||

112A | Contains double edges | |||||

112B | Contains
double edges Same as Cube-112B and Icosahedron-112B | |||||

115x | ||||||

117x | ||||||

120x | Contains double edges | |||||

121x | ||||||

132A | Contains double edges | |||||

132B | Contains double edges | |||||

135A | Contains double edges | |||||

135B | Contains double edges | |||||

135C | ||||||

135D | ||||||

135E | ||||||

135F | ||||||

135G | Same as Cube-135A and Icosahedron-135B | |||||

135H | ||||||

135I | ||||||

135x | Contains double edges | |||||

136 | Contains double edges | |||||

136x | Contains double edges | |||||

138x | ||||||

144A | Contains double edges | |||||

144B | Contains double edges | |||||

144C | Contains double edges | |||||

144D | Contains double edges | |||||

144E | Contains
double edges Same as Cube-144D and Icosahedron-144C | |||||

147xA | ||||||

147xB | ||||||

153x | Contains double edges | |||||

160x | ||||||

162A | Contains double edges | |||||

162B | Contains double edges | |||||

162C | ||||||

162D | ||||||

165A | Same as Cube-165A and Icosahedron-165D | |||||

165B | Contains double edges | |||||

165C | Contains double edges | |||||

165D | ||||||

165E | ||||||

168xA | ||||||

168xB | ||||||

168xC | ||||||

171A | ||||||

171B | ||||||

174x | ||||||

180A | Contains double edges | |||||

180B | Contains double edges | |||||

180C | Contains double edges | |||||

180D | Contains double edges | |||||

180E | Contains
double edges Same as Cube-180 and Icosahedron-180 | |||||

183A | Contains double edges | |||||

183B | Contains double edges | |||||

187x | Contains double edges | |||||

189x | ||||||

192A | ||||||

192B | ||||||

192C | Contains double edges | |||||

192x | Contains double edges | |||||

198A | ||||||

198B | ||||||

198C | ||||||

198D | ||||||

198E | ||||||

198F | ||||||

198G | Same as Cube-198A and Icosahedron-198B | |||||

198H | ||||||

198I |