Regular icosahedron surface tours

by
Jan Kristian Haugland

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Other polyhedra: Tetrahedron Cube Octahedron

Here is a collection of (presumably) all regular icosahedron 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.

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

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

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

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

8 | Same as Cube-8 | |||||

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

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

15 | ||||||

16 | Same as Cube-16 | |||||

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

20 | Same as Cube-20 | |||||

24A | ||||||

24B | Same as Cube-24B | |||||

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

25 | ||||||

28 | ||||||

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

36 | Same as Cube-36B | |||||

40A | ||||||

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

44 | Same as Cube-44B | |||||

45A | Same as Cube-45B | |||||

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

48A | ||||||

48B | ||||||

56A | Same as Cube-56C | |||||

56B | ||||||

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

63A | 3D
printed model for sale at Shapeways | |||||

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

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

64 | ||||||

68A | Same as Cube-68A | |||||

68B | Same as Cube-68B | |||||

70A | ||||||

70B | ||||||

76A | ||||||

76B | ||||||

80A | ||||||

80B | ||||||

80C | ||||||

81 | ||||||

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

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

90A | ||||||

90B | ||||||

90C | ||||||

92 | ||||||

96A | ||||||

96B | Same as Cube-96D | |||||

96C | ||||||

100A | ||||||

100B | ||||||

100C | ||||||

105 | ||||||

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

108B | Same as Cube-108B | |||||

108C | Same as Cube-108D | |||||

108D | ||||||

110 | ||||||

112A | ||||||

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

114 | ||||||

120A | ||||||

120B | ||||||

120C | ||||||

124A | ||||||

124B | ||||||

128 | Same as Cube-128D | |||||

129 | ||||||

135A | Same as Cube-135C | |||||

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

135C | Same as Cube-135B | |||||

136A | ||||||

136B | ||||||

144A | ||||||

144B | Same as Cube-144C | |||||

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

145 | ||||||

150 | ||||||

162 | ||||||

164A | Same as Cube-164A | |||||

164B | Same as Cube-164B | |||||

165A | ||||||

165B | ||||||

165C | Same as Cube-165B | |||||

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

168A | ||||||

168B | ||||||

172A | ||||||

172B | ||||||

175 | ||||||

176 | ||||||

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

184 | Same as Cube-184C | |||||

185 | ||||||

192A | ||||||

192B | ||||||

195A | ||||||

195B | ||||||

195C | ||||||

195D | ||||||

195E | ||||||

198A | Same as Cube-198B | |||||

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

200 | Same as Cube-200D |