Hello Kurt !
This functionality is in fact just a “normal embed” based on an iframe with custom url parameters, which you can find on this page.
However, please note that the specific parameters used to reproduce the behaviour of Sketchfab homepage are only available for certain pricing plans:
transparent: set a transparent background for the embeds (Pro and +).
ui_controls: hide the bottom controls (Premium and +).
ui_watermark_link: remove the link on the Sketchfab logo (Business and Enterprise)
ui_watermark: remove the Sketchfab logo (Enterprise)
Note that you can have a preview of those if you use an iframe in a local .html file located on your computer, no matter what your plan is.
If you are curious, I’ve attached to this post a dead-simple example (index.zip (671 Bytes) ) embedding one of your models (very nice one by the way! ) over some background text. Just download it and open it with your usual browser to see get an idea of the possible render.
Of course, hosting this page online will ignore the url parameters reserved to superior pricing plans.
Don’t hesitate to let me know if something was not clear, or to contact us through this form if you could be interested in an Enterprise plan.