I am trying to get VertexCoordinates of this picture of the problem https://artofproblemsolving.com/wiki/index.php/2022_AMC_10A_Problems/Problem_21?fbclid=IwAR2bdHwJEpjarZEwope1hYOcnnXqnvzae38Y8ZrfWKCKQunfAuT9s30q32o

I tried with syntax PolyhedronData["Dodecahedron", "VertexCoordinates"] but I do not know the name of Polyhedron. How can I get VertexCoordinates of this polyhedron?

enter image description here


1 Answer 1


That looks like half of a truncated octahedron.

truncOctVertices = PolyhedronData["TruncatedOctahedron", "VertexCoordinates"]

will get you all of the vertex coordinates.

We can filter to get just the lower half (z value nonpositive):

lowHalfVertices = Select[truncOctVertices, NonPositive@*Last]

We can visualize to confirm:


enter image description here

  • $\begingroup$ How can I get FaceIndices by usingPolyhedronData["lowHalfVertices", "FaceIndices"]? $\endgroup$ Dec 22, 2022 at 1:48
  • $\begingroup$ What are you trying to do? FaceIndices would give you insight into Mathematica's representation of a polyhedron, and that seems sort of out of left field based on your original question. Also, once we've turned it into a BoundaryMeshRegion, we have a different representation. There are functions that allow you to extract data from mesh regions: MeshPrimitives, MeshCells, MeshCoordinates, and yes, MeshCellIndex. $\endgroup$
    – lericr
    Dec 22, 2022 at 2:08

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.