Radiant Cut Diamond
The Radiant Cut is a mixed fancy cut - combining aspects of both Round Brilliant Cut and Emerald Cut designs. The Original Radiant Cut was invented by Henry Grossbard in 1977 with the goal of enabling people to choose a square or oblong diamond with the sparkle of a brilliant.  It has both step cut and brilliant cut facets.
Many new diamond cuts have been devised since the advent of computer design technology - but there are few designers who can claim to have invented a new diamond shape without computer assistance. Grossbard's Radiant Cut was one such design. He said, famously, "I didn't use math. I used diamonds." Originally protected by one of the first patents ever awarded to a diamond cut, the design of the Radiant is now public domain. It has similarities with the Princess Cut - but the Radiant has cropped corners like an Emerald Cut, and a different arrangement of facets.
Radiant Cut Diamond Design Details
The original Radiant Cut diamond has 70 facets, but a wide variety of modified Radiant Cuts now exist - with varying facet arrangements  - such as the "Gabrielle" Radiant seen to the left. Stanley Grossbard (son of Henry) says that most Radiants now have 66 facets. The stones are often cut with the "eye-pleasing" Length / Width ratio of 1:1.5 - although the ratio and "rectangularity" varies with Radiants and can be anywhere from fully square to rectangular. 
Although many people think that the only difference between a Radiant Cut and a Princess Cut diamond is that the Radiant has had the corners removed, the inventor of the Radiant disputes this vigorously and states that the true Radiant is a very different cut which reflects light in a very different way. 
As of the current time, the GIA describes Radiant Cut diamonds as either "cut corner rectangular modified brilliant" or "cut corner square modified brilliant", and does not issue a "cut grade" on radiants.  One of the reasons for this is that due to the higher complexities of the cut proportions and facets of the Radiant Cut, a grading system would be difficult. 
"Gabrielle" Radiant Cut diamond ring
Grossbard also contends that the original Radiant was designed not to maximise the weight retention of the stone, but to create the most beautiful diamond he could. He said that true Radiants are flatter as opposed to deeper, and there is a higher degree of internal reflection in an Original Radiant Cut than in a round diamond due to the resulting increase in the number of times the light reflects within the stone.
In the last 30 years the world has seen an explosion of new fancy shapes and square diamonds inspired by the Radiant Cut - and a resurgence in popularity of square diamonds as a result. But the Grossbards also stated in a November 2004 magazine article that they had struggled to promote and defend the Original Radiant Cut design against a "sea of imitations", and that "The GIA certificate is insufficient to assess the quality of a Radiant cut." 
The Radiant has enjoyed much popularity in recent times - and has been worn by celebrities. It's reported that Hilary Duff, Brooke Mueller and Khloe Kardashian have all received radiant-cut diamond engagement rings. 
Diagram of a Radiant diamond's facets
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Note - this website is intended for general informational and entertainment purposes, and should not be considered to be professional consultation. If you are considering purchasing precious stones, be sure to seek the advice of a qualified professional.