Put text in Graphics3D syntax?

Question

Some friends from the forum helped me to make this MMA script, I have tried to modify it to put text similar to the image, perhaps with a more beautiful letter, but I can't think of how, I have seen in the forum and in the help of MMA.

I looked in the forum and in the MMA help and the closest thing I found is this

 myarrow[begin_List, end_List, mytext_String] := Graphics3D[
 {Arrow[{begin, end}],Text[Style[mytext, 14], end]}]


 Graphics3D[Cylinder[], 
 Epilog -> 
 Inset[Framed[Style["Cylinder", 20], 
 Background -> LightYellow], {Right, Bottom}, {Right, Bottom}]]

I need this, you have to run the code to see where it is, the text is supposed to rotate along with the figure, it is attached to the planes, the image only represents a frontal view of the movement

Clear["Global`*"];
img = Import["https://i.sstatic.net/FAbVi.png"];
colors = DominantColors[img];
c = 1/2 (1 + Sqrt[5]);
xy = {{1, c, 0}, {-1, c, 0}, {-1, -c, 0}, {1, -c, 0}};
yz = {{0, 1, c}, {0, -1, c}, {0, -1, -c}, {0, 1, -c}};
zx = {{c, 0, 1}, {c, 0, -1}, {-c, 0, -1}, {-c, 0, 1}};
options = {Boxed -> False, SphericalRegion -> True, 
Lighting -> {{"Ambient", White}}};
g = Graphics3D[{AbsolutePointSize[8], Point /@ {xy, yz, zx}, 
colors[[5]], Polygon[xy], colors[[4]], Polygon[yz], colors[[3]], 
Polygon[zx], EdgeForm[Thick], FaceForm[], 
ConvexHullMesh@Catenate[{xy, yz, zx}]}, options];
rotZ = Table[
Graphics3D[
GeometricTransformation[First@g, RotationTransform[t, {0, 0, 1}]],
 options], {t, 0, 2 \[Pi], .2}];
 rotY = Table[
Graphics3D[
GeometricTransformation[First@g, RotationTransform[t, {0, 1, 0}]],
 options], {t, 0, 2 \[Pi], .2}];
rotX = Table[
Graphics3D[
GeometricTransformation[First@g, RotationTransform[t, {1, 0, 0}]],
 options], {t, 0, 2 \[Pi], .2}];
ListAnimate[Catenate[{rotZ, rotY, rotX}], AnimationRate -> 6]

I would appreciate a hand, I would be grateful

Answer 1

Using the approach from this answer to construct the polygons and lines:

cp = Map[Prepend[0]]@Delete[{{3}, {6}}]@CirclePoints[{1, Pi/3}, 6];

coords = Table[Map[RotateRight[#, i - 1] &]@cp, {i, 3}];

colors = {RGBColor[1, .5, .5], RGBColor[1, 1, .5], RGBColor[.5, 1, .5]};

Transform text primitives to 3D coordinates by processing the output from BoundaryDiscretizeGraphics:

ClearAll[textCoords]
textCoords[string_, cbounds_ : {{-1/2, 1/2}, {1/2, 5/6}}, padding_ : .2] := 
  Module[{tc = (MeshPrimitives[
         BoundaryDiscretizeGraphics[Text[string], _Text], 1, 
         Multicells -> True] /. Line[x_] :> Line[Join @@ x])[[All, 1]]}, 
    Map[Map[Prepend[0] @* 
     RescalingTransform[(1 + padding) CoordinateBounds @ tc, cbounds]]] @ tc];

labels = {"2nd Mathematical Olympiad", "B C M H K", "2023"};

textcoordinates = MapIndexed[{x, y} |-> 
   Map[Map[RotateRight[#, -1 + First @ y] &]][
      textCoords[Style[x, FontFamily -> "Times"]]]] @ labels;

show = Show[Graphics3D @
   Thread[{AbsoluteThickness[1/2], Black, Map[Line] @ textcoordinates, 
     colors, Lighting -> {{"Ambient", White}}, Polygon /@ coords}], 
  MeshConnectivityGraph @ ConvexHullRegion[Join @@ coords], 
  SphericalRegion -> True, Boxed -> False, 
  PlotRange -> 1, ImageSize -> Large, ImagePadding -> 5]

Animation above produced using

rotate[angle_, axis_] := MapAt[Rotate[#, angle, UnitVector[3, axis]] &, {1}]

frames = Join @@ Table[rotate[2 Pi t, a]@show, {a, 1, 3, 1}, {t, 0, 1, 1/18}];

Export["MathOlympiad.gif", frames]

Notes:

$Version
"13.3.0 for Linux x86 (64-bit) (June 3, 2023)"

Ignore the red syntax highlighting of Multicells -> True.