Eduard Bobik describes some non-convex space fillers on his interesting website. Here is a shape that he calls a cross space filler.

- Cut out many copies of the pattern pieces. You will use two pattern pieces to make one polyhedron. The pattern piece with one tab is the top of the polyhedron and the one with many tabs is the bottom.
- Score and crease. The dashed lines are valley folds, the dot-dashed lines are mountain folds.
- Glue the tab for each pattern piece to the neighboring edge.
- Glue the top half and bottom half together to form a star-shaped polyhedron.
- Glue the polyhedra together to fill space.

- The coordinates for the cross space filler are: A(-1, 1, 0)

B(1, 1, 0)

C(1, -1, 0)

D(-1, -1, 0)

E(0, 0.5, 0)

F(0.5, 0, 0)

G(0,-0.5, 0)

H(-0.5, 0, 0)

I(0, 0, 1)

J(0, 0, -1)

Faces:

AEI

BIE

BFI

CIF

CGI

DIG

DHI

AIH

AEJ

BJE

BFJ

CJF

CGJ

DJG

DHJ

AJH

- The information on this page is from Edo Bobik's very informative and interesting website.
- Maurice Starck discusses space fillers and much more on his extensive website with interactive models.

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