You can't really answer this question without acknowledging the parallel development paths for high-quality 3D graphics, which includes not only the dominant Polygon/Texture-mapping approach, but also the Ray Tracing approach. This parallel development path continues through today, with recent announcements like Nvidia's next generation RTX platform, that features real-time Ray Tracing.
While the LDS-1 is a very early example of being purpose-built for 3D graphics, it was incapable of producing anything photo-realistic or "natural". At roughly the same time, Ray Tracing was being used for high quality static images that, while taking many hours to render, produced results with a level of quality that would still impress 3D artists today.
In 1982, Osaka University created a purpose-built supercomputer designed for 3D graphics rendering using Ray Tracing. The supercomputer was known as the LINKS-1 Computer Graphics System, and was an early contender for fastest computer in the world. It is briefly described on Wikipedia as:
a massively parallel processing computer system with 514 microprocessors (257 Zilog Z8001's and 257 iAPX 86's), used for rendering realistic 3D computer graphics with high-speed ray tracing.
The Japanese supercomputer predates SGI's commercialization of the Geometry Engine by 5 years, and could produce far better 3D graphics.
Of course, both supercomputers and SGI systems were far out-of-reach for users of Desktop computer systems of the 1980s. However, Ray Tracing enjoyed a brief popularity at this time. Most 3D artists relied on affordable Amigas with accelerator boards that included FPUs to render 3D graphics and animations using ray tracing. The Macintosh II, with its Motorola 68020/68881 CPU/FPU, was also popular for this purpose. There is available a tremendous amount of early 3D desktop computer content created with such equipment, using both ray tracing and polygon rendering techniques. In a sense, any 1980s machine with an FPU was an "accelerated 3D graphics workstation", if 3D rendering software made use of it. My own Amiga 1000 had a 68881 FPU attached via the side-expansion bus for just this purpose, in 1988, at the same time SGI was selling the IRIS 3000-series.