The Genco "Wedge", as it is labeled, is probably what you have. And, there are a ton of them in circulation. They must have been popular in their day. I have never seen a true wedge made by Genco, and the razor labeled "Wedge" by Genco that I refer to is a near wedge that is labeled "Wedge."

But, pictures will tell the story.

My experience with Genco "Wedge" razor is very positive. They shave oddly, and don't feel as sharp as a full hollow. This is probably more due to the feeling of a near wedge than any Genco-specific. When I first tried, I thought I hadn't honed the razor well. But, it shaved well. So, what do they say... the shave test is the final test!