// Hollow Dodecahedron
// A regular dodecahedron or pentagonal dodecahedron is a dodecahedron composed of regular pentagonal faces, three meeting at each vertex. This example shows constructing the individual faces of the dodecahedron and extruding inwards.

// Set units
@settings(defaultLengthUnit = in)

// Input parameters
// circumscribed radius
circR = 25

// Calculated parameters
// thickness of the dodecahedron
wallThickness = circR * 0.2

// angle between faces in radians
dihedral = acos(-(sqrt(5) / 5))

// inscribed radius
inscR = circR / 15 * sqrt(75 + 30 * sqrt(5))

// pentagon edge length
edgeL = 4 * circR / (sqrt(3) * (1 + sqrt(5)))

// pentagon radius
pentR = edgeL / 2 / sin(toRadians(36))

// Define a plane for the bottom angled face
plane = {
  plane = {
    origin = [
      -inscR * cos(toRadians(toDegrees(dihedral) - 90)),
      0,
      inscR - (inscR * sin(toRadians(toDegrees(dihedral) - 90)))
    ],
    xAxis = [cos(dihedral), 0.0, sin(dihedral)],
    yAxis = [0, 1, 0],
    zAxis = [sin(dihedral), 0, -cos(dihedral)]
  }
}

// Create a regular pentagon inscribed in a circle of radius pentR
bottomFace = startSketchOn(XY)
  |> polygon({
       radius = pentR,
       numSides = 5,
       center = [0, 0],
       inscribed = true
     }, %)

bottomSideFace = startSketchOn(plane)
  |> polygon({
       radius = pentR,
       numSides = 5,
       center = [0, 0],
       inscribed = true
     }, %)

// Extrude the faces in each plane
bottom = extrude(bottomFace, length = wallThickness)
bottomSide = extrude(bottomSideFace, length = wallThickness)

// Pattern the sides so we have a full dodecahedron
bottomBowl = patternCircular3d(
  bottomSide,
  instances = 5,
  axis = [0, 0, 1],
  center = [0, 0, 0],
  arcDegrees = 360,
  rotateDuplicates = true,
)

// pattern the bottom to create the top face
patternCircular3d(
  bottom,
  instances = 2,
  axis = [0, 1, 0],
  center = [0, 0, inscR],
  arcDegrees = 360,
  rotateDuplicates = true,
)

// pattern the bottom angled faces to create the top
patternCircular3d(
  bottomBowl,
  instances = 2,
  axis = [0, 1, 0],
  center = [0, 0, inscR],
  arcDegrees = 360,
  rotateDuplicates = true,
)