Create a Geometric Fashion Brand Logo

Craft a logo for a high-end fashion brand that embodies geometric design. The logo should consist of elegant, abstract shapes like diamonds and hexagons arranged in a unique composition. Utilize a sophisticated color palette, such as black, white, and rich jewel tones, to evoke luxury. The interaction between the geometric forms should suggest a sense of stylishness and modernity. The brand name should be written in a sleek, minimalist font to complete the upscale aesthetic. The brand name is: GeoChic.