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This question is a continuation of the previous one：

How to draw a cube?

Draw a cube, ABCD-A1B1C1D1, with the length of the edge as 1. How to draw this cube and establish a space rectangular coordinate system at the same time. Point A on the bottom is the origin of the coordinate system, the line AB is on the x-axis, the line AD is on the y-axis, and the line AA1 is on the z-axis.

After establishing the spatial rectangular coordinate system, the coordinates of each vertex of the cube are known.How can I get the coordinates of a vector composed of any two vertices? Can I get it automatically?

For example, if you input vector AB, you can get the coordinate AB of vector AB={1,0,0}and so on...

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reg = Parallelepiped[{0, 0, 0}, {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}]; pts = MeshPrimitives[reg, 0]; g = HighlightMesh[ reg, {Labeled[0, "Index"], Style[2, Directive[White, Opacity[.1]]]}]

enter image description here

  • For two points,for example 6 and 4.
v[6, 4] = pts[[;; , 1]][[6]] - pts[[;; , 1]][[4]] With[{i = 6, j = 4}, Graphics3D[{{White, Lighting -> {{"Ambient", White}}, g}, Red, Arrow[{pts[[;; , 1]][[i]], pts[[;; , 1]][[j]]}]}, Boxed -> False]]

enter image description here

  • Labeled
HighlightMesh[reg, {Labeled[{0, 1}, Style["A", Red, 15]], Labeled[{0, 2}, Style["B", 15]], Labeled[{0, 4}, Style["D", 15]], Labeled[{0, 5}, Style["A1", 15]], Labeled[{0, 6}, Style["E", 15]], Style[2, Directive[White, Opacity[.1]]]}]

enter image description here

  • We can also use Graphics3D+Text to draw such picture, but here we let it be a exercise.
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  • $\begingroup$ Can't we mark the corresponding letters on the vertices? $\endgroup$ Commented Jan 30, 2023 at 1:59

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