How many regular dodecahedra does it take to make the regular FourSpace "solid" that has them as its "faces"?

* ''120.  It's called a 120-Cell (how imaginative!) and you can find out about it here: http://mathworld.wolfram.com/120-Cell.html''

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To expand somewhat ...

Take a regular tetrahedron, glue another onto each face giving five in total, and it will fold nicely through FourSpace to give a HyperPentahedron.

Take a regular hexahedron - also known as a cube - glue another onto each face giving seven in total, and it will fold nicely through FourSpace to give a Tesseract with a hyperface missing. Glue that extra cube in place and you have a hypercube.

The same game can be played with the regular dodecahedron, and the question is, how many hyperfaces does it have?  How many dodecahedra are needed for it to fold around and close up neatly?

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It is really difficult to "visualize" turning around a plane. Interesting. I never thought about it before. 

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CategoryMath