1, 2, 3, 4, 5, 6, 7, 8, 9, 10

[Ed Pegg]

What is this finite sequence?
1, 2, 3, 4, 5, 6, 7, 8, 9, 10  

For a unit edge truncated octahedron, the set of squared diagonal lengths.  
The full set is 0, 1, 1, 1, 2, 3, 3, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 7, 7, 8, 9, 9, 9, 10

What are other examples of simple finite sequences that come from unexpected 
sources?

[Allan Wechsler]

The corresponding multiset for the tetrahedron is 0, 1^3.

For the cube, it's 0, 1^3, 2^3, 3.

For the octahedron it's 0, 1^4, 2.

But what about the icosahedron? It's lots of ugly surds, right?

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