Impossible Staircase — Penrose Study detector
Sixteen solid treads form a closed route with a positive rise at every step. A complete ascending cycle has no consistent levels.
Click the visible surface to select a piece; drag to move it. Labelled handles resize along the solid’s own axes; the green handle rotates. Hold Shift to bypass snapping, or Alt to move a piece apart from its joints.
Keyboard: arrows move; Shift+arrows move by 10 px; Delete removes; Ctrl+D duplicates; Ctrl+Z / Ctrl+Shift+Z undo and redo.
Click joints to build connected lines. Drag a yellow midpoint to curve a segment; drag a blue joint to reshape adjacent segments. Enter or double-click finishes. Click the first joint to close a path. Shift snaps new points to the grid.
Tip: crisp, connected lines give the clearest clues. Nothing is uploaded to a server.
Reconstruct and inspect in 3D
Inspect closed solid pieces with their exact dimensions, shared vertices and 3D connection equations. Uploads fit visible piece silhouettes; unsupported pictures use surface boundaries. Partial versions omit conflicting pieces or surfaces; possible versions leave incompatible joins disconnected. Your image stays on your device.
Constructed locally from indexed solid primitives by ShapeKeeper. No reference image pixels are used.
Inspect the pieces and their connections
The intended stair route closes, but every transition requires a positive rise.
Adding those rises around the cycle cannot return to the starting height.
This construction contains 16 solid pieces and 0 named port connections. Select a piece to change its dimensions, drag it to move its connected group, or detach a joint before changing that part independently. The analyzer checks the edited geometry each time; the example name does not determine its verdict.
Every transition in this staircase requires a positive rise. The analyzer follows the directed tread route and rejects a cycle that returns to its starting tread after ascending.
Read the Impossible Staircase — Penrose Study drawing guide, then try your own construction in the impossible shapes detector. The reconstruction method explains how solid dimensions, image fitting and connection equations contribute different evidence.
Compare the source view with a rotating model
Build partial version removes pieces at contradictory joins. Build possible version retains the individual solids while leaving conflicting joins disconnected. Neither forces an impossible connection by stretching a piece. Download the model as OBJ, or keep editable dimensions and joints with Save assembly. Share, PNG and PDF preserve a result locally.
Raster uploads are fitted from their visible silhouette and colour regions. A recognized complete construction supplies its intended connection rules only after the pixel fit succeeds. Separate fitted primitives remain separate. An unfamiliar picture can leave hidden structure unresolved; see how to inspect an ambiguous drawing.
Compare Impossible Trident / Blivet, Impossible Pentagon — Beam Study and Impossible Arch — Joinery Study to examine how different piece arrangements change the joints and openings.
For further editing experiments, open Impossible Trident / Blivet, Impossible Pentagon — Beam Study or Impossible Crate — Cube Variant and compare their closure equations after detaching a connection.
The Impossible Staircase — Penrose Study example gives the same editable construction with its geometric explanation.