Consider the tetrahedron with vertices at:
$$(0,0,0)$$ $$(2,-\sqrt2,0)$$ $$(2,\sqrt2,0)$$ $$(2,0,2)$$
This tetrahedron is not regular but does it have any notable properties? It appears to have some symmetries. For example, its faces are congruent. Its two long edges appear somehow symmetrical with respect to each other (and separate mutually perpendicular faces). Does the tetrahedron have a name?
Sometimes it's called a tetragonal disphenoid, sometimes a digonal antiprism. However it is only an isogonal polyhedron.
--- rk