Is there any interest in creating a FEM Julia organization?

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That’s a good question, I will investigate some more on that. There is a general cellular homology theory

So the answer is yes, it seems that hyper cubes are possible to represent with a simplicial set… it is closely tied together with the CW-complex. Simplicial set is a generalization, taking unions of subspaces.

For example, if we have 4 vertices (to make a square) we might use v12 - v14 + v23 + v34 to represent the boundary of the square by using 1-simplices. So I’d say you can represent them… you can also get that result by computing (on master) the boundary of the 2-cube square v123 + v134 itself:

julia> using Grassmann, Leibniz; @basis tangent(ℝ^4,2,4); #master branch

julia> ∂(v1234) # boundary of 3-simplex
0 - 1∂₄v₁₂₃ + 1∂₃v₁₂₄ - 1∂₂v₁₃₄ + 1∂₁v₂₃₄

julia> ∂(v123+v134) # boundary of 2-cube
0 + 1∂₃v₁₂ - 1∂₂v₁₃ + 1∂₄v₁₃ - 1∂₃v₁₄ + 1∂₁v₂₃ + 1∂₁v₃₄

Note the extra edges 1∂₄v₁₃ - 1∂₂v₁₃ which cancel out if you set ∂ᵢ = ∂ⱼ for i≠j so it works.