You see, there is a man who came up with some 3D printed connector thingys that work with dowels to build any of the five platonic solids.
http://www.thingiverse.com/thing:9359/apps/#apps
You can go to that website and download the instructions for 3D printing all of the connector thingys. And have a great time building the shapes as big or small as you want!
What are the Platonic Solids? They are 3 dimensional shapes where
- each face is the same regular polygon
- the same number of polygons meet at each corner (vertex)
This person came up with a way to 3D print the corners or vertices (many vertex) so that you can make these varied shapes. They could be small table top models or big enough to sleep in. What a great way to spend an afternoon, building these volumes with the various vertices!
There are instructions on the webpage, here http://www.thingiverse.com/thing:9359/#files for printing the vertices.
Meanwhile, for a little more information about Platonic Solids.
There are only 5 platonic solids, these include:
Tetrahedron: This one is based on triangles. Three triangles meet at each corner or vertex.
Cube: This one is based on squares. Three squares meet at each vertex.
Octahedron: This one is based on triangles again, but this time four triangles meet at each corner or vertex.
Decahedron: This one is based on pentagons, where three pentagons meet at each corner or vertex.
Icosahedron: This one is based on triangles again, where five triangles meet at each corner or vertex.
If you want to try to make these shapes in origami, there are some folks who have figure them out! Go to this math and origami site to see some incredible examples: https://mathigon.org/origami to see examples of origami platonic solids and other complex polygons.
And go to https://www.mathsisfun.com/geometry/model-construction-tips.html to find paper model templates.