I think the erroneous mental image I was using was of trying to pack equilateral triangular prisms rather than tetrahedrons. Just didn't think about it properly.
How many equilateral tetrahedra can be connected together without any empty space between them?
- Thread starter Olga
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exchemist
Valued Senior Member
That was what I posted in post 2 of this thread.Had to look this up.
Apparently, no.
"In geometry, tetrahedron packing is the problem of arranging identical regular tetrahedra throughout three-dimensional space so as to fill the maximum possible fraction of space.
The currently densest known packing structure for regular tetrahedra is a double lattice of triangular bipyramids and fills 85.63% of space
Currently, the best lower bound achieved on the optimal packing fraction of regular tetrahedra is 85.63%."
Tetrahedron packing - Wikipedia
en.wikipedia.org
But my fault for not including explanatory text - which you have now supplied.
My earlier replies to this thread were about the question in the OP and spin-offs from that. I only noticed yesterday that the OP question is a completely different question to the one in the thread title.That was what I posted in post 2 of this thread.
But my fault for not including explanatory text - which you have now supplied.