Tolkowski's flower cuts were developed in the late 1980s and introduced in 1988 at the World Federation of Diamond Bourses Congress by De Beers. In an effort to to encourage their industry-wide use, DeBeers has not patented them.
The flower cuts are the Marigold, the Dahlia, the Zinna, the Sunflower, and the Fire Rose cut, and they were designed to increase yield and brilliance in shallow diamond crystals that are unsuitable for the traditional diamond shapes. Leo Smams, head cutter for Argyle diamonds of Australia, has experimented with these and other cuts to provide a good balance of color and light for the lighter shades of colored diamonds mined there, but the diamond trade in general has been slow to accept them.
The Marigold is octagonal, with step facetting of both crown and pavillion. The Dahlia is an oval variant with large pavillion facets. The Zinnia is round with a cluster of small facets on the pavillion near the culet. The Sunflower is shaped like a squarish octagonal emerald cut but without the step facetting of the pavillion. The Fire Rose is six-sided with a cluster of small facets on the pavillion near the culet and a star pattern to the crown facets. All of these cuts have large tables. These are incomplete descriptions but cover the most striking features and I hope they give you some idea of what the cuts look like.