3D projection of a 4-dimensional dodecahedron, the '120 cell'




This object is the ‘truncated 120 cell’, a 3D projection or shadow of a 4-dimensional shape. The shape is the 4D analogue of a dodecahedron, composed of 120 truncated dodecahedra and 600 tetrahedra. In 4-space all of the dodecahedra have correct geometry, however as a consequence of the projection into 3-space all but the central dodecahedra are distorted. For a similar reason the 2D shadow of a cube is made of rhombi instead of squares. The 120 cell has 2 types of symmetry, 10 axes of the first type (one for each pair of vertices of the central dodecahedron) and 6 of the second type (one for each pair of faces of the central dodecahedron). This model is a modified version of an .STL file created by George Hart. It took 17 hours on the Form 1, and it’s the most complex print I’ve created so far. If you’re interested in the geometry of these objects, this paper by George Hart explains them in greater detail.

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