  Recently self-affine sponges have been shown to be interesting
counter-examples to several previously open problems. One class of recently
studied sponges are Bedford-McMullen sponges with a weak coordinate ordering
condition, that is, sponges with several coordinates having the same
contraction ratio. The Assouad type dimensions of such sets cannot be
calculated using the same formula as the regular Bedford-McMullen sponges. We
calculate the Assouad type dimensions for such sponges and the more general
Lalley-Gatzouras sponges with a weak coordinate ordering condition, discussing
some of their more subtle details along the way.
