Impossible Triangle Key & Controller Hanger for SKÅDIS - Real Penrose Illusion

Yes, it really is an impossible triangle, and it really holds your keys and your controller. A key and game-controller hanger for the IKEA SKÅDIS pegboard, shaped as the Penrose triangle. It is a real 3D object: three bars that form an open zig-zag. From one exact spot in front of the board the far end of the bottom bar hides perfectly behind the near end of the left bar, so the triangle looks closed and seems to float with nothing holding it. Step to the side and the trick shows: the two ends are 58 mm apart.

Details

• Triangle about 100 mm wide, bars 18 mm, three shades of blue like a shaded drawing. Small HANMA logo inlaid flush on the right bar.

• The viewpoint is calculated for an eye at 1.50 m, 1.00 m in front of the board, with the clip row at 1.30 m. The geometry uses a projective transform toward that eye, so the edges line up in true perspective, not just from far away. The OpenSCAD file is parametric: change the eye height, distance or clip height and re-export.

• Four key hooks (alternating 48 and 62 mm long so neighbouring rings never clash), chamfered on top, with a raised tip.

• A game controller (Xbox-size, 152 × 107 × 61 mm) sits on top of the apex. It rests on a hidden tongue behind the top corner and leans on the board.

• Everything that holds it (back plate with the clips, two 8 × 8 mm pegs, the controller tongue) sits exactly in the "shadow" of the bars as seen from the viewpoint, so you cannot see it from there.

• Sticks out about 115 mm from the board.

Printing

• One plate for the A1 mini with the AMS lite (160 × 121 × 62 mm), no supports: triangle, back plate with hooks and 3 clips (2 + 1 spare).

• 3 colours, but the light and medium blue only live in the first 12 mm; above that it is a single colour, so few colour changes.

• Bambu Studio: 4 h 25 min, 65 g (light 15.1 g, medium 17.1 g, dark 32.8 g, purge included).

• The triangle prints lying on the two side bars with the bottom bar rising at 35°; the logo is on the bed face, so it comes out flat and sharp.

Mounting

1. Push the two clips into the pockets at the top of the back plate, hold it 8 mm high, push the clips through two slots of one row (40 mm apart) and let it drop. Mount that row at about 1.30 m.

2. Slide the triangle onto the two pegs, pushing it toward the board. The pegs rise 11.6° toward the viewer, so gravity pushes it in; no glue needed. To take it off, lift it along the pegs.

3. Stand 1 m away with your eye at 1.50 m, close one eye (or use your phone camera) and move a little until the corner closes.

How it was checked

• The illusion, in a 2D projection (own z-buffer, 0.1 mm pixels) from the exact eye point: the silhouette matches the ideal impossible triangle (0 differing pixels away from edges, IoU 1.0000), it encloses exactly 1 hole (the loop is closed) and none of the support shows (plate, pegs, tongue, clips: 0 pixels). Two points 58 mm apart in 3D land on the same image spot (0.0001 mm). Controls: from the side the loop opens (0 holes) and 1375 mm² of support become visible; with the eye 10 cm to the side the joint opens 6.3 mm.

• Tolerance: moving your eye 10 mm gives a 0.6 mm step at the joint; 10 mm farther away only 0.13 mm. With both eyes open each eye sees about 2 mm, so it works best with one eye or a camera.

• Pegboard fit (common SKÅDIS test): clips go in raised 7.8 mm and drop without touching (0.000 mm³); mounted clips cannot be pulled out (90.5 mm³) or pushed in without lifting (64.1 mm³); the assembly hangs without touching (0.000 mm³) and cannot come forward (231 mm³).

• Assembly: the triangle slides 30 mm along the pegs without touching (0.000 mm³), seats at the bottom of the sockets (0.6 mm more collides: 51 mm³) and cannot drop or come straight out (79 / 14 mm³).

• Controller rests on the tongue and the board without touching anything else (0.000 mm³); 0.5 mm lower or further back it collides (88 / 7 mm³). Four key rings hang without touching each other or anything else (0.000 mm³).

• Physics (masses from the slicer grams, controller 280 g, 4 × 60 g of keys): along the pegs gravity pushes the triangle in with 0.64 N (control: designed for an eye below the piece it would push it out). The controller's centre of mass is 10.8 mm behind the front edge of its support (control: 3 cm further out it would tip). Clips: total load 5.73 N, moment 0.302 N·m, each clip hook pulls 8.9 N, about 6 MPa in the hook (×4.9 margin); both clips carry weight (3.37 N and 2.35 N). Pegs: 0.93 MPa bending (×16).

• No overhangs over 45° except the 5 mm bridges over the clip pockets; the colour bodies do not overlap (0 mm³). OpenSCAD source included.

Español

Colgador de llaves y de mando para IKEA SKÅDIS con forma de triángulo imposible de Penrose. Es un objeto 3D real abierto: desde el punto exacto (ojo a 1,50 m, a 1 m del tablero) los dos extremos, separados 58 mm, coinciden y el triángulo parece cerrado y flotando; desde un lado se ve el truco. Cuatro ganchos de llaves y un mando encima, apoyado en una lengüeta escondida. Una placa del A1 mini: 4 h 25 min, 65 g, sin soportes.

العربية

علاقة مفاتيح ويد تحكم للوح IKEA SKÅDIS على شكل مثلث بنروز المستحيل. إنه جسم ثلاثي الأبعاد حقيقي ومفتوح: من النقطة الدقيقة (العين على ارتفاع 1.50 م وعلى بعد متر من اللوح) يلتقي الطرفان المتباعدان 58 مم فيبدو المثلث مغلقا ومعلقا في الهواء، ومن الجانب تنكشف الخدعة. أربعة خطافات للمفاتيح ويد تحكم فوقه على لسان مخفي. لوح واحد لطابعة A1 mini: 4 ساعات و25 دقيقة، 65 غ، بدون دعامات.