Super Tetrahedron
This image shows a large tetrahedron of linear dimension four, made from twenty tetrahedra of linear dimension one:
How many additional Platonic solids of linear dimension one would be required to fill in all the holes?
Image credit: http://www.fmbr.org/
The answer is 14.
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1 solution
You would need 4 additional unit tetrahedra and 10 additional unit octahedra to fill in all the holes.
The 4 tetrahedra are inserted upside down, one on the third row and three on the bottom row. Then the remaining holes can be filled perfectly with 10 octahedra: 6 on the bottom row, 3 on the third row, and 1 on the second row.
4 + 1 0 = 1 4