diamond shapes can also (apparently, but never by me!) be called lozenge shaped.

a quick check in OneLook, reveled diamond shaped alternated between first and second meaning (with a medical 'tablet' of the same shape, sometimes being the alternate first meaning )

i had always thought of lozenge as a sucking type candy to sooth a sore throat, or to ease coughing. (and hadn't thought about the shape, or that the shape was a key factor between a cough lozenge (brand X) and cough drop, (brand Y)

one dictionary suggest the word lozenge is actual related to the word rhombus!
(a diamond shape could be defined as a rhombus with equal sides, and paired angles, (opposite angles at 60° (apx) or 120° (apx).)

i stumbled across this use of the word lozenge when looking for information about striped patterns and/or harliquin patterns. (at one point, i described the diamond shaped element of my stained glass as having a harliquine type design, and the person i was speaking to, didn't understand what i meant by a harliquine type pattern!--i think they would be less likely to understand a lozenge type pattern!--or is that just me, (ie, a personal knowledge gap?)