# Prime Boxes for the Clip Pentakedge

A polykedge is a solid made of equal cubes joined face to face or edge to edge or both. A prime box for a polycube or polykedge is a rectangular prism, or box, that the polycube or polykedge can tile, and which cannot be dissected into smaller prime boxes. A polycube or polykedge can have at most finitely many prime boxes.

Here I list known prime boxes for the Clip Pentakedge in order of dimensions. The number of tilings shown is independent of rotations and reflections. For more information about box tilings by this tile, see this page by Torsten Sillke.

Torsten Sillke has proved by coloring that this piece can tile only boxes whose volume is a multiple of 15. Only such boxes are shown here.

TilesDimensionsTilingsFinder
243×4×106Torsten Sillke
603×4×25168Torsten Sillke
363×6×1068Torsten Sillke
543×6×15799Torsten Sillke
423×7×1010
633×7×152865
723×8×15
543×9×10548
813×9×15
993×11×15
244×5×61Torsten Sillke
844×7×15
964×8×15
1084×9×15
1324×11×15
665×6×11
845×6×14
1025×6×17
845×7×12
2105×7×30
725×8×9
905×9×10 Helmut Postl
1505×10×15 Helmut Postl
Impossible
M×N
M×N
3×3×NTorsten Sillke
3×4×5
3×4×15Torsten Sillke
3×5×NTorsten Sillke
4×4×NTorsten Sillke
4×5×N,
N ≢ 0 (mod 6)
5×5×NTorsten Sillke
5×6×6
5×6×7
5×6×9
5×6×10
5×6×13
5×7×9
5×7×15
5×7×18
5×7×21
5×7×27Helmut Postl
5×9×9
5×9×11Helmut Postl
5×9×12
5×9×13
5×9×14
5×9×15
5×9×17

Last revised 2022-04-13.

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Col. George Sicherman [ HOME | MAIL ]