Ancient Greeks knew about them; the Platonic Solids are fascinating. You can read all about them here:  https://en.wikipedia.org/wiki/Platonic_solid

These are edge shapes of the 5 Platonic Solids. See the photograph of the drawing by Leonardo da Vinci for Luca Pacioli's 1509 book De Divina Proportione (The Divine Proportion). These models match the drawing.

The solid shapes are here.
The stick and ball shapes are here. 
The hyperbolic shapes are here.
The Kleetope shapes are here.
The Safe Kleetope shapes are here.
The 25 Christmas Ornaments are here.
The edge shapes are here. <this page>
The hyper shapes are here.
A chart explaining the Platonic Solids is here.

To print use the *.3mf files or:

1. scale 2000%

2. rotate to print on a face

3. use paint on supports

The OpenSCAD source file is included.