# The sandpiles on the beach

Puzzling Asked on January 2, 2022

We call a convex polyhedron a sandpile if one of the faces, called base, has a common edge with all the other faces. Furthermore, each vertex is linked with three edges. We consider the sandpiles by vertex translations, rotations and symmetries close. Therefore, there are 3 sandpiles with a hexagonal base:

How many sandpiles have a base with 9 edges?

27

Answered by Brian Hopkins on January 2, 2022

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