I would go for 'regular isosceles tetrahedron', or 'stretched tetrahedron' or better still, just call it by the name of the package. However, if one triangle is iscoceles, does the other have to be also? If 'opposite pairs' are the same, is that pair x the same and pair y the same but different, or do they have to be the same as well?

Warning: I'm not a mathematician, and I think maths is boring...