From what I have learnt, $\Delta$-complexes seem fantastic compared to simplicial complexes, since they have much fewer vertices and edges and thus are easier to compute homology.
I am aware that simplicial complexes are $\Delta$-complexes, but not the other way around.
Are there any drawbacks of $\Delta$-complexes that we need to be aware of? To put it in another way, is there anything we can do with simplicial complexes but not for $\Delta$-complexes?
Thanks.