# How to get vertices of each face of the 80th Johnson solid?

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.

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

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

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


Triangles and rectangles:

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


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

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

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


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]


and a simpler command

PolyhedronData[{"Johnson", 80}]


produces a nicer result.

• Graphics3D[{Glow[Yellow], EdgeForm[Gray], PolyhedronData["Johnson", 80]}, Lighting -> None] produces an empty plot in red. Commented Feb 5, 2021 at 9:17
• 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. Commented Feb 5, 2021 at 9:54
• It should be noticed the command Graphics3D[{Glow[Yellow], EdgeForm[Gray], PolyhedronData["Johnson", "Polygons"]}, Lighting -> None] produces no messages, but an incorrect plot. Commented Feb 5, 2021 at 16:21