diff --git a/Main.hs b/Main.hs
index 83532fe..802ff8f 100644
--- a/Main.hs
+++ b/Main.hs
@@ -6,7 +6,7 @@ import Debug.Trace (trace)
 import Math.NumberTheory.Roots (integerSquareRoot, integerCubeRoot)
 
 type Cell = Int  -- ^ The index of a cell in the cube
-type Layer = Int -- ^ A layer of our cube
+type Peel = Int -- ^ A peel of our cube
 type Ring = Int -- ^ A ring of a 2D spiral
 type Length = Int -- ^ The length of an line segment
 type X = Int
@@ -24,7 +24,10 @@ cube a = a * a * a
 ring :: Cell -> Ring
 ring o = integerSquareRoot o `div` 2
 
-edge :: Layer -> Length
+peel :: Cell -> Peel
+peel c = integerCubeRoot c `div` 2
+
+edge :: Peel -> Length
 edge l = 2 * l + 2
 
 atZ :: Z -> Point2D -> Point3D
@@ -36,11 +39,17 @@ reflectY (x, y) = (x, -y - 1)
 reflectX :: Point2D -> Point2D
 reflectX (x, y) = (-x - 1, y)
 
+reflectX3 :: Point3D -> Point3D
+reflectX3 (x, y, z) = (-x - 1, y, z)
+
+reflectZ3 :: Point3D -> Point3D
+reflectZ3 (x, y, z) = (x, y, -z - 1)
+
 rotate :: Length -> Point2D -> Point2D
 rotate l (x, y) = (-y - 1, -x - 1)
 
-location :: Length -> Cell -> Point3D
-location l c = atZ h $ case h `mod` 4 of
+spirals :: Length -> Cell -> Point3D
+spirals l c = atZ h $ case h `mod` 4 of
     0 -> growingSpiral l o
     1 -> rotate l $ shrinkingSpiral l o
     2 -> reflectX . reflectY $ growingSpiral l o
@@ -62,12 +71,39 @@ growingSpiral l o | o == 0         = (0, 0)
 shrinkingSpiral :: Length -> Cell -> Point2D
 shrinkingSpiral l o = growingSpiral l (area l - o - 1)
 
+peeledCubes :: Length -> Cell -> Point3D
+peeledCubes _ c | o < a = reverseIfOdd
+                        . atZ (e `div` 2 - 1) -- on top of the cube
+                        $ growingSpiral e o
+                | o < a + (e - 2) * (e - 1) * 4
+                        = reverseIfOdd
+                        $ mantel p e (o - a)
+                | otherwise
+                        = reverseIfOdd
+                        . atZ (-e `div` 2) -- on the bottom of the cube
+                        . reflectX
+                        $ shrinkingSpiral e (o - a - (e - 2) * (e - 1) * 4)
+  where p = peel c -- ^ the current peel
+        o = c - cube (edge $ p - 1) -- ^ offset within the current peel
+        e = edge p -- ^ the length of the edge of the current peel
+        a = area e -- ^ the area of a side of the current peel
+        reverseIfOdd = if p `mod` 2 == 0 then id else (reflectX3 . reflectZ3)
+
+mantel :: Peel -> Length -> Cell -> Point3D
+mantel p e m | o <= r             = (p - r + o, 0 - p - 1, p - r - 1)
+             | o <= r +     e - 1 = (p, 0 - p - 1 + o - r, p - r - 1)
+             | o <= r + 2 * e - 2 = (p - o + r + e - 1, p, p - r - 1)
+             | o <= r + 3 * e - 3 = (0 - p - 1, p - o + r + 2 * e - 2, p - r - 1)
+             | otherwise          = (0 - p - 1 + o - r - 3 * e + 3, 0 - p - 1, p - r - 1)
+  where r = m `div` (4 * e - 4) -- ^ revolutions since starting on the side
+        o = m - (4 * e - 4) * r -- ^ offset within this revolution
+
 asMatrix :: Length -> [[[Cell]]]
 asMatrix e = foldl (\c (i, x, y, z) -> replace c z $ replace (c!!z) y $ replace (c!!z!!y) x i)
                    (replicate e $ replicate e $ replicate e (-1))
-                   [ (i, x + div e 2, y + div e 2, z)
+                   [ (i, x + div e 2, y + div e 2, z + div e 2)
                    | i <- [0..cube e - 1]
-                   , let (x, y, z) = location e i
+                   , let (x, y, z) = peeledCubes e i
                    ]
   where replace :: [a] -> Int -> a -> [a]
         replace l i e = take i l ++ [e] ++ drop (i+1) l