Edges of the 4_21 polytope

Question

How to get the edges of the $4_{21}$ polytope? Given the vertices, and given that it is convex, I can theoretically get them with the R package cxhull. But there are 240 vertices of dimension 8, and my laptop crashes...

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EDIT

I managed to get them with the Python library pycddlib.

Answer 1

In fact, there's no need of a computational geometry library. Two vertices are connected if and only if their squared distance is 8 (I don't know why).

R code:

edges <- NULL
for(i in 1L:(nrow(vertices)-1L)){
  v1 <- vertices[i, ]
  for(j in (i+1L):nrow(vertices)){
    v2 <- vertices[j, ]
    if(c(crossprod(v1-v2)) == 8){
      edges <- rbind(edges, c(i, j))
    }
  }
}