Your concern is only with the cut, not the colour, correct? If so, I do not see anything deficient from the single frontal view. I would request a hand shot though just in case. The lighting used seems unusually strong and may mask a darker stone that pictured when viewed in person.
PS
You may want to resize your signature picture as it is HUGE.
I would describe the cut as simple and also question the lighting. While it looks to be an appealing green, there are dark spots and I wonder how it would look (extinction, color) were it not to have bright light shining directly, and seemingly unevenly, on it.