Space-Filling Bisymmetric Hendecahedron

Only a few of Platonic and Archimedean solids can be stacked together to fill space without leaving gaps. Guy Inchbald described five interesting solids that stack together in surprising ways. Here is one solid with eleven faces (hendecaedron) that is a space-filling solid.

Steps

1. Print the pattern from Guy Inchbald's website.
   
2. Cut out, fold up and glue together multiple copies. The photo above uses twelve solids.
   
3. Glue together four bisymmetric hendecahedra to make what Inchbald refers to as a "boat."
   
4. Stack these boats together to fill space.
   

Notes

• The coordinates for the vertices of the bisymmetric hendecahedron are: A( 0, 0, 2)
  B( 2, 1, 1)
  C( 0,-1, 1)
  D(-2, 1, 1)
  E( 0, 2, 0)
  F( 1,-1, 0)
  G(-1,-1, 0)
  H( 2, 1,-1)
  J( 0,-1,-1)
  K(-2, 1,-1)
  L( 0, 0,-2)
  
  Faces:
  ABED
  ABFC
  ACGD
  BEH
  BHF
  CFJG
  DGK
  DKE
  EKLH
  FHLJ
  GJLK
  
  

Links

• This site has an interactive model of the hendecahedron.
• Guy Inchbald reprints his Mathematical Gazette article on his website.

References

• (Inchbald 1996)