Three dodecahedra with an edge in common
If we put three regular dodecahedra around a vertex, there will be some holes because the sum of the dihedral angles is smaller than 360°. Likewise, the sum of the angles of three regular pentagons is smaller than 360°. So, if we put three regular pentagons around a vertex there will be some holes and these holes allow the pentagons of a net of the dodecahedron to fold up in the 3-dimensional space to form a dodecahedron. In the same way, the holes in this image allow a net of the 120-cell to fold up in the 4-dimensional space.
Image appeared in the survey "Officina della matematica" in the double number 4-5 of the magazine XlaTangente.
© matematita
immagine di Gian Marco Todesco
The image belongs to the sections...:
Dodecahedron (3D geometry)
Number 4-5 (From "XlaTangente")
Various matters (4D geometry)
Further information:
http://www.toonz.com/personal/todesco
