Loop

This is the puzzle idea I had: you get many identical copies of a polycube, with road segments drawn on some of the faces. You are instructed to assemble them to fill a square footprint with the visible road segments forming a single loop. As you do, a complex landscape comes together[1].

The tool below lets you explore different pieces on square boards of different sizes. For each piece-board combination, there are some number of solutions. Within a solution, you can select the rim height- this a raised ledge that goes around the outer perimeter and hides side faces[2].

Piece

Unfixable

    Fixable

      Solution

      Scores

      Interesting Findings

      Finding Score Solution Board Pieces ◯
      Loop      		 ★
      Unique      		 ⊘
      Dead Ends      		 ↯
      Faults      		 🞑
      Rects      		 ◩
      Asym      		 ◐
      2color      		 Notes
      The only FBB solution 87 FBB_6x6_1_0 6x6 5 yes yes no 0 0 yes yes FBB fits no other floor up to 10x10, and this is its only 6x6 layout.
      Top ★ Loop 96 PQA_8x8_790_0 8x8 12 yes yes no 0 0 no no Ranked first. Very symmetrical. uses all 12 orientations! looks cool/complex.
      Cute mini ★ Loop solution 88 BAV_6x6_2_0 6x6 6 yes yes no 0 0 no no every base used exactly 2x
      Top ★ Loop Asymmetrical (fallback) 80 PQA_8x8_730_0 8x8 12 yes yes no 2 6 yes yes ranked 7th. cons: translated patterns, already used PQA in Top ★ Loop
      compact asymmetric puzzle 80 P_4x4_476_0 4x4 6 yes yes no 1 1 yes yes Unique: with its loop marking on every piece, solving all P 4x4 layouts finds only this one.
      Loopy Trucks 79 Y2_8x8_569_0 8x8 8 yes yes no 2 3 yes yes all circles viewed from above
      Wavy Trucks 78 Y2_8x8_978_0 8x8 8 yes yes no 2 3 no yes wavy diagonal lines
      The only Tx2 8x8 solution 90 Tx2_8x8_1_1 8x8 12 yes yes yes 0 0 no no This one actually is manually 2-colorable.
      Top ★ Loop Asymmetrical 85 PLR+_6x6_198_0 6x6 10 yes yes yes 1 4 yes no Ranked 3rd but best of the top 10.
      Top PQO ★ Loop 89 PQO_6x6_1460_2 6x6 8 yes yes yes 0 1 no no The best of PQO's 11 unique loops. It has a loop only at rims 2 and 3, and checking every layout at rim 2 finds only this one.
      Two G Islands 86 G_6x6_241_0 6x6 8 yes no yes 1 0 yes no Pattern fits other G 6x6 solutions (so no ★). Need to examine all solutions before printing. Islands are in-place reversible.
      Cute mini ★ Loop solution 78 A2_6x6_20_0 6x6 6 yes yes yes 1 2 no no

      1. With roads curving up onto vertical surfaces, as seen in the surreal city geometry of Inception (2010), Doctor Strange (2016), Control Resonant (2026), etc. ↩ī¸Ž

      2. Imagine the pieces of this puzzle come in a box, with instructions to assemble it inside the box. The rim height is the unit height of the inside of that box. Hiding some faces allows for different solutions; in some cases it reduces the number of possibilities and in others it increases them. ↩ī¸Ž