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I am trying to draw the 80th Johnson solid by LaTeX; I tried

PolyhedronData[{"Johnson", 80}]

and

PolyhedronData[{"Johnson", 80}, "Vertices"]

To draw this solid, I must determine the vertices of each face. How to find them?

P.S. I use Mathematica 11.2.

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    $\begingroup$ PolyhedronData[{"Johnson", 8}, {"Vertices", "FaceIndices"}] $\endgroup$
    – cvgmt
    Feb 5, 2021 at 9:03
  • $\begingroup$ BTW, I don't see {"Johnson", 80} in the output of PolyhedronData[]. $\endgroup$
    – user64494
    Feb 5, 2021 at 18:35

2 Answers 2

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{vertices, faceindices} = PolyhedronData[{"Johnson", 80}, {"Vertices", "Faces"}];

Graphics3D[{RandomColor[], Opacity[.7], Polygon[vertices[[#]]]} & /@ faceindices,
  Boxed -> False]

enter image description here

Triangles and rectangles:

Row @ Table[Graphics3D[{RandomColor[], Opacity[.7], Polygon[vertices[[#]]]} & /@
     Select[faceindices, Length@# == k &],
  Boxed -> False, ImageSize -> Medium], {k, {3, 4}}]

enter image description here

Note: In versions 12.0+, replace "Faces" with "FaceIndices".

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Too long for a comment. Unfortunately, concerning its plot, the result of

Graphics3D[{Glow[Yellow], EdgeForm[Gray], PolyhedronData["Johnson", "Polygons"]}, Lighting -> None]

enter image description here

is not satisfactory. I followed the documentation.

Addition. It appears the right command is

Graphics3D[{ Glow[Yellow], EdgeForm[Gray], 
PolyhedronData[{"Johnson", 80}, "Polygons"]}, Lighting -> None]

enter image description here and a simpler command

PolyhedronData[{"Johnson", 80}]

enter image description here

produces a nicer result.

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  • $\begingroup$ Graphics3D[{Glow[Yellow], EdgeForm[Gray], PolyhedronData["Johnson", 80]}, Lighting -> None] produces an empty plot in red. $\endgroup$
    – user64494
    Feb 5, 2021 at 9:17
  • $\begingroup$ The result of Graphics3D[{Opacity[0.3], Glow[Yellow], EdgeForm[Gray], PolyhedronData["Johnson", "Polygons"]}, Lighting -> None] is unsatifactory too. I understand there are self-intersections here. Unfortunately, I don't find any example of such kind in the documentation. $\endgroup$
    – user64494
    Feb 5, 2021 at 9:54
  • $\begingroup$ It should be noticed the command Graphics3D[{Glow[Yellow], EdgeForm[Gray], PolyhedronData["Johnson", "Polygons"]}, Lighting -> None] produces no messages, but an incorrect plot. $\endgroup$
    – user64494
    Feb 5, 2021 at 16:21

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