ft_24_cell.lua

local gizmo_size = 0.75
local alpha = 0.3

local function def_ft_24_cell(id, name, depths, piece_types_fn)
  puzzles:add{
    id = id,
    version = '0.1.0',
    name = name,
    ndim = 4,
    build = function(p)
      local sym = cd'f4'
      local ooox = sym.ooox.unit

      -- Build shape
      p:carve(sym:orbit(ooox))
      local t = {
        'Mono Triad [1]',
        'Mono Triad [2]',
        'Mono Triad [3]',
        'Red Triad [1]',
        'Red Triad [2]',
        'Red Triad [3]',
        'Orange Triad [1]',
        'Orange Triad [2]',
        'Orange Triad [3]',
        'Yellow Triad [1]',
        'Yellow Triad [2]',
        'Yellow Triad [3]',
        'Green Triad [1]',
        'Green Triad [2]',
        'Green Triad [3]',
        'Blue Triad [1]',
        'Blue Triad [2]',
        'Blue Triad [3]',
        'Purple Triad [1]',
        'Purple Triad [2]',
        'Purple Triad [3]',
        'Magenta Triad [1]',
        'Magenta Triad [2]',
        'Magenta Triad [3]',
      }
      p.colors:set_defaults(t)

      -- Define axes and slices
      p.axes:add(sym:orbit(ooox), depths)
      p.axes:autoname()

      -- Define twists
      local a1 = p.axes[ooox]
      local a2 = sym:thru(4):transform(a1)
      local a3 = sym:thru(3):transform(a2)
      local a4 = sym:thru(2):transform(a3)
      local t = sym:thru(2, 1)
      for _, axis1, axis2, twist_transform in sym.chiral:orbit(a1, a2, t) do
        p.twists:add(axis1, twist_transform, {
          name = axis2.name,
          gizmo_pole_distance = (1+2*alpha)/sqrt(3) * gizmo_size,
        })
      end

      local ridge = a2.vector + a3.vector -- ridge orthogonal to `a1`
      local init_transform = sym:thru(3, 1) -- rot{fix = a1.vector ^ ridge, angle = PI}
      for t, axis1, _ridge, twist_transform in sym.chiral:orbit(a1, ridge, init_transform) do
        p.twists:add(axis1, twist_transform, {
          name = t:transform(a2).name .. t:transform(a3).name,
          gizmo_pole_distance = (1+alpha)/sqrt(2) * gizmo_size,
        })
      end

      local edge = ridge + a4.vector -- edge orthogonal to `a1`
      local init_transform = sym:thru(3, 2)
      for t, axis1, _edge, twist_transform in sym.chiral:orbit(a1, edge, init_transform) do
        p.twists:add(axis1, twist_transform, {
          name = t:transform(a2).name .. t:transform(a3).name .. t:transform(a4).name,
          gizmo_pole_distance = gizmo_size,
        })
      end

      if piece_types_fn then
        piece_types_fn(p)
      end
    end,

    tags = {
      author = {"Milo Jacquet", "Andrew Farkas"},
      experimental = true,
    },
  }
end

def_ft_24_cell('ft_24_cell_shallow', "Facet-Turning 24-cell (Shallow)", {INF, 2/3}, function(self)
  local sym = cd'f4'
  lib.utils.unpack_named(_ENV, self.axes)

  local ax1 = A
  local cell_sym = symmetry{
    sym:thru(1),
    sym:thru(2),
    sym:thru(3),
  }
  self:mark_piece(A(1) & ~cell_sym:orbit(G(1)):union(), 'center', "Center")
  self:mark_piece(X(1) & M(1) & ~O(1) & ~S(1) & ~Q(1), 'ridge', "Ridge")
  self:mark_piece(X(1) & M(1) & O(1) & ~T(1) & ~S(1) & ~U(1) & ~Q(1) & ~J(1) & ~H(1), 'edge', "Edge")
  self:mark_piece(X(1) & M(1) & O(1) & ~T(1) & Q(1) & ~H(1), 'edgelet', "Edgelet")
  self:mark_piece(X(1) & ~H(1) & O(1) & T(1) & M(1) & Q(1), 'subcorner', "Subcorner")
  self:mark_piece(X(1) & H(1) & O(1) & T(1) & M(1) & Q(1), 'corner', "Corner")
  self:unify_piece_types(sym)
end)
def_ft_24_cell('ft_24_cell_half_cut', "Facet-Turning 24-cell (Half-Cut)", {INF, 0, -INF})