Round brilliant is the most common cut for engagement diamonds, so there will be lots of choices in the marketplace.
Some women will want something different. Perhaps a square cushion, or a marquise (and no, the "s" is not silent as in "marquee").
Some diamond cuts
For cuts such as an oval, heart, pear, brilliant pear, emerald cut, rectangle cut and the marquise, consider several factors.
The length : width ratio is not only important to the eye, but can be a long term breakage issue. A long and skinny cut, especially a marquise, can break much easier than one of better proportions.
A general rule is, don't select a stone that has a length more than 2 times the width. A ratio of 1.5 - 2 is considered an ideal range. Anything under 1.5 will tend to look stubby. Be aware that corners can break / chip much easier on a rectangle than an emerald cut. And probably the most durable of the non-round cuts is the oval.
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