How to plot tetrahedron inscribed in cube?

[michaelfortunato]

Hi, was wondering how to achieve this diagram in CeTZ?
Thanks

[michaelfortunato]

#import "@local/mnf-typst:0.1.0": mnf_ams_article, theorem, definition, remark, theorem, proof, example, subpar
#import "@preview/cetz:0.3.4": canvas, draw, vector
#import "@preview/cetz-plot:0.1.1": plot

#show: mnf_ams_article.with(title: [Tetrahedron In A Cube])

#let dashed-line(..args) = {
  import draw: *
  line(..args, stroke: (dash: "dashed"))
}
#align(center)[
  #canvas({
    import draw: *
    let O = (0, 0, 0)
    let i = (1, 0, 0)
    let j = (0, 1, 0)
    let k = (0, 0, 1)
    let size = 5
    let vertices = ()
    for x_direction in (-1, 1) {
      let x_delta = vector.scale(i, size / 2 * x_direction)
      for y_direction in (-1, 1) {
        let y_delta = vector.scale(j, size / 2 * y_direction)
        for z_direction in (-1, 1) {
          let z_delta = vector.scale(k, size / 2 * z_direction)
          let vertex = vector.add(vector.add(vector.add(O, x_delta), y_delta), z_delta)
          vertices.push(vertex)
        }
      }
    }
    let (v1, v2, v3, v4, v5, v6, v7, v8) = vertices
    rotate(y: -5deg)
    dashed-line(v1, v2)
    line(v3, v4)
    dashed-line(v1, v3)

    line(v5, v6)
    dashed-line(v5, v7)
    line(v7, v8)
    content(v1, [$v_(1)$], anchor: "north")
    content(v2, [$v_(2)$], anchor: "east")
    content(v3, [$v_(3)$], anchor: "south")
    content(v4, [$v_(4)$], anchor: "east")
    content(v5, [$v_(5)$], anchor: "north")
    content(v6, [$v_(6)$], anchor: "north-west")
    content(v7, [$v_(7)$], anchor: "south-west")

    dashed-line(v1, v5, stroke: (dash: "dashed"), name: "AB")
    line(v3, v7)
    line(v5, v3, stroke: (paint: red, dash: "dashed"))
    line(v2, v5, stroke: (paint: red))
    line(v3, v8, stroke: (paint: red))
    line(v3, v2, stroke: (paint: red))
    line(v8, v5, stroke: (paint: red))
    on-layer(
      1,
      {
        line(v2, v8, stroke: (paint: red))
        line(v2, v6)
        line(v4, v8)
        line(v2, v4)
        line(v6, v8)
        content(v8, [$v_(8)$], anchor: "south", padding: .2)
      },
    )
  })
]