Four-Axis Cube Spin, Hyperboloid

####Four-Axis Cube Spin

The cube has four major axes connecting four pairs of vertices. What if we spin the cube around all the four axes and allow the solids to merge in space? Well, we get a nice-looking shape.

The design attached is based on 37 copies of a 50-mm cube around each axis. It can be printed in two pieces to avoid using extensive support. For the curious mind, what is its surface area or volume? What are all the symmetries?

####References

1. https://www.thingiverse.com/thing:3015098
2. https://www.thingiverse.com/thing:3151990
3. https://www.thingiverse.com/thing:3517442
4. https://www.thingiverse.com/thing:3921545