WOLFRAM|DEMONSTRATIONS PROJECT

An Unfoldable Polyhedron

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radius of circumscribedinner triangle
0.3
height of inner triangle
0.2
height of hat
1
spiky
hat
net of hat
new random net
To unfold a polyhedron, cut it along some edges and flatten it out to form a net. (Allowing cuts on faces as well as edges is called a general unfolding.)
This Demonstration shows a "spiked tetrahedron" of Bern et al. [1]. It can only be unfolded with overlaps since one quarter of it (a "hat") can be unfolded only with overlaps.