Post #1894641
2023-03-11 18:31 UTC
We can fold a net into a dodecahedron as in a paper model. If faces can intersect, we can further fold it to a new shape. 12 original faces overlap to get only 6 unique faces, with one as base and 5 side faces. It can be seen as a stellated pentagonal pyramid.
The stellated pentagonal pyramid isn't a real polyhedron because some edges belong to only one face. In a real polyhedron, each edge must belong to exactly two faces.
Replies (1)
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@nanma80@mathstodon.xyz 2023-03-11 18:32
If we start from a different net, we can get the great dodecahedron where all 12 faces are distinct. The stellated pentagonal pyramid contains half (6) of the 12 faces of the great dodecahedron. If we start from others net of the dodecahedron, we may get a shape with between 6 and 12 faces.