Weight systems defining five-dimensional reflexive polyhedra. You can search by Hodge numbers and Euler characteristic: enter one, two, or three numbers! Three of the numbers fix the others by the following relations:

chi = 48 + 6 (h^1,1 − h^1,2 + h^1,3)
h^2,2 = 44 + 4 h^1,1 − 2 h^1,2 + 4 h^1,3

After entering the numbers press "Retrieve". The subsequent list of properties and weight systems will update. A full list of weight systems and a list of possible properties will be accessible if the number of matching weight systems is small enough.

Weight systems defining five-dimensional non-reflexive polyhedra. You can search by vertex count n_v, facet count n_f, and point count n_p: enter one, two, or all three numbers!

After entering the numbers press "Retrieve". The subsequent list of properties and weight systems will update. A full list of weight systems and a list of possible properties will be accessible if the number of matching weight systems is small enough.