SnipFold

Regular Icosahedron

Twenty exact equilateral triangles in five connected four-face panels, with fifteen matched glue seams and a hinged closing flap.

Materials

  • 160-180 gsm paper
  • Scissors
  • Ruler and blunt scoring tool
  • Pencil
  • Tacky PVA glue
  • Blunt craft stick

Finished size: 68.05 x 64.72 x 76.08 mm; edge 40 mm

Steps

CutValley foldMountain foldGlue area

  1. Cut, identify, and score five panels

    Print at 100%; check the 50 mm ruler. Cut P1-P5 once each, keeping every shaded tab. Keep the printed side outside. Before folding, pencil the seam numbers from the following table beside BOTH matching edges. Coordinates are edge midpoints in mm: x right and y up from the lower-left corner of the CUT OUTLINE bounding box, with the piece oriented exactly as printed. Use a ruler; coordinates identify edges, not new cuts. Each panel has four triangles in a chain. Score all dashed folds.

  2. Mark seam S01

    S01: shaded TAB edge midpoint P1 (20.0, 5.0) joins plain RECEIVING edge midpoint P5 (10.0, 17.3). Write this same number beside both edges. Glue is applied to the outside of the 5 mm tab; it will lie under the receiving face.

  3. Mark seam S02

    S02: shaded TAB edge midpoint P1 (10.0, 22.3) joins plain RECEIVING edge midpoint P2 (20.0, 0.0). Write this same number beside both edges. Glue is applied to the outside of the 5 mm tab; it will lie under the receiving face.

  4. Mark seam S03

    S03: shaded TAB edge midpoint P2 (10.0, 17.3) joins plain RECEIVING edge midpoint P3 (20.0, 0.0). Write this same number beside both edges. Glue is applied to the outside of the 5 mm tab; it will lie under the receiving face.

  5. Mark seam S04

    S04: shaded TAB edge midpoint P3 (10.0, 17.3) joins plain RECEIVING edge midpoint P4 (20.0, 0.0). Write this same number beside both edges. Glue is applied to the outside of the 5 mm tab; it will lie under the receiving face.

  6. Mark seam S05

    S05: shaded TAB edge midpoint P4 (10.0, 17.3) joins plain RECEIVING edge midpoint P5 (20.0, 0.0). Write this same number beside both edges. Glue is applied to the outside of the 5 mm tab; it will lie under the receiving face.

  7. Mark seam S06

    S06: shaded TAB edge midpoint P1 (50.0, 22.3) joins plain RECEIVING edge midpoint P5 (30.0, 52.0). Write this same number beside both edges. Glue is applied to the outside of the 5 mm tab; it will lie under the receiving face.

  8. Mark seam S07

    S07: shaded TAB edge midpoint P1 (30.0, 57.0) joins plain RECEIVING edge midpoint P2 (50.0, 17.3). Write this same number beside both edges. Glue is applied to the outside of the 5 mm tab; it will lie under the receiving face.

  9. Mark seam S08

    S08: shaded TAB edge midpoint P2 (30.0, 52.0) joins plain RECEIVING edge midpoint P3 (50.0, 17.3). Write this same number beside both edges. Glue is applied to the outside of the 5 mm tab; it will lie under the receiving face.

  10. Mark seam S09

    S09: shaded TAB edge midpoint P3 (30.0, 52.0) joins plain RECEIVING edge midpoint P4 (50.0, 17.3). Write this same number beside both edges. Glue is applied to the outside of the 5 mm tab; it will lie under the receiving face.

  11. Mark seam S10

    S10: shaded TAB edge midpoint P4 (30.0, 52.0) joins plain RECEIVING edge midpoint P5 (50.0, 17.3). Write this same number beside both edges. Glue is applied to the outside of the 5 mm tab; it will lie under the receiving face.

  12. Mark seam S11

    S11: shaded TAB edge midpoint P1 (70.0, 57.0) joins plain RECEIVING edge midpoint P5 (60.0, 69.3). Write this same number beside both edges. Glue is applied to the outside of the 5 mm tab; it will lie under the receiving face. Reserve this seam for the final flap.

  13. Mark seam S12

    S12: shaded TAB edge midpoint P1 (60.0, 74.3) joins plain RECEIVING edge midpoint P2 (70.0, 52.0). Write this same number beside both edges. Glue is applied to the outside of the 5 mm tab; it will lie under the receiving face.

  14. Mark seam S13

    S13: shaded TAB edge midpoint P2 (60.0, 69.3) joins plain RECEIVING edge midpoint P3 (70.0, 52.0). Write this same number beside both edges. Glue is applied to the outside of the 5 mm tab; it will lie under the receiving face.

  15. Mark seam S14

    S14: shaded TAB edge midpoint P3 (60.0, 69.3) joins plain RECEIVING edge midpoint P4 (70.0, 52.0). Write this same number beside both edges. Glue is applied to the outside of the 5 mm tab; it will lie under the receiving face.

  16. Mark seam S15

    S15: shaded TAB edge midpoint P4 (60.0, 69.3) joins plain RECEIVING edge midpoint P5 (70.0, 52.0). Write this same number beside both edges. Glue is applied to the outside of the 5 mm tab; it will lie under the receiving face. Reserve this seam for the final flap.

  17. Pre-fold the rigid triangles

    Mountain-fold all structural hinges by 41.81 degrees from flat (138.19 degrees inside). Fold tabs inward to the same angle. Dry fit without glue; never curve or stretch a triangle. On P5, keep the end triangle bounded by S11 and S15 swung open as the access flap.

  18. Add panel P2

    Join seams S02, S07, S12 with P2. Match the numbered edges exactly, tuck each tab under its receiving triangle, and use a thin film of PVA. Press each seam from inside while the shell is open; let each joint grab before continuing. Keep the P5 end flap open even after the upper shell is joined; a blunt craft stick through that opening supports the last upper seams.

  19. Add panel P3

    Join seams S03, S08, S13 with P3. Match the numbered edges exactly, tuck each tab under its receiving triangle, and use a thin film of PVA. Press each seam from inside while the shell is open; let each joint grab before continuing. Keep the P5 end flap open even after the upper shell is joined; a blunt craft stick through that opening supports the last upper seams.

  20. Add panel P4

    Join seams S04, S09, S14 with P4. Match the numbered edges exactly, tuck each tab under its receiving triangle, and use a thin film of PVA. Press each seam from inside while the shell is open; let each joint grab before continuing. Keep the P5 end flap open even after the upper shell is joined; a blunt craft stick through that opening supports the last upper seams.

  21. Add panel P5

    Join seams S01, S05, S06, S10 with P5. Match the numbered edges exactly, tuck each tab under its receiving triangle, and use a thin film of PVA. Press each seam from inside while the shell is open; let each joint grab before continuing. Keep the P5 end flap open even after the upper shell is joined; a blunt craft stick through that opening supports the last upper seams.

  22. Close the accessible bottom flap last

    After all other seams dry, dry-fit the P5 flap over receiving tabs S11, S15. With the flap still open, coat those two exposed tab faces lightly with tacky PVA and wait until tacky. Swing the hinged triangle onto both tabs from outside; do not insert a tab into a sealed shell. Support the opposite faces in your palm and lightly burnish both closing edges from outside. Hold until set; do not crush the unsupported flap. Paper thickness and adhesive working time require a physical trial.

Notes

The 3D model shows each piece in its finished, idealized shape; the exploded view only spreads the pieces apart. It is not a paper-physics simulation: curved shapes are forming guides, not exact physical folding or proof of developability, and intermediate fold shapes are not supplied.