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For example, for a $4$-dimensional cube of size length $10$ this set would be $\{(x,y,z,t)|0 \leq x,y,z,t \leq 10 \land x,y,z,t \in \mathbb{Z}\}$

I am interested in this structure but all online references I can find use terms like "$n$-cube" to mean just the vertices, or the surface of this cube, but I am interested in the set containing its interior points, too.

aellab
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  • What properties are you interested in? That should narrow it down if this set has a special name. – Sonal_sqrt Mar 03 '23 at 09:04
  • The set of integer points inside an $n$-dimensional cube of side length $x$ (an explicit example is given in the question body) – aellab Mar 03 '23 at 09:12

1 Answers1

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Generally I see the term "lattice points" used for integer coefficients, here is an example where they talk about how many lattice points are in a lattice cube (Three dimensional cube where all the vertices are lattice points)

lattice cube

Note: the term "lattice" is one of the more overloaded terms in math/physics/chemistry. This is just one of many of them.

Alan
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