Polytropes in TA3

A polytrope is a tropical polytope which at the same time is convex in the ordinary sense. The following tabular shows the tropical equivalence classes of 3-dimensional polytropes, where m is the number of pseudovertices of a 3-dimensional polytrope, lying between 4 and 20, and t3(m) is the number of the tropical equivalence classes of 3-polytropes with exactly m pseudovertices.

For further information please take a look at the paper Tropical and ordinary convexity combined (by Michael Joswig and Katja Kulas), preprint, arxiv: 0801.4835, to appear in Adv. Geometry.

Pictures of Polytropes in TA3
m   t3(m)
4 1
5 1
6 4
7 3
8 20
9 14
10 39
11 43
12 68
13 54
14 74
15 53
16 43
17 21
18 17
19 8
20 5