triangles

Med
Lrg

Description :

'Jitterbug' of a triangle tiling of the plane. The different colour
triangles have opposite orientations.
view triangle tiling animation (3Mb)





tri octahedra

Med
Lrg

Description :

Octahedra have their faces attached above the triangles of one
orientation and below the triangles of the other orientation. The
transformation of the triangle tiling transforms the octahedra in
their layers. At the maximum expansion the empty space forms
cuboctahedra, and these cuboctahedra close down to form a pair of
tetrahedra at the minimum expansion.
The following animations show a 3x3x3 lattice of octahedra.
view animation with fixed plane (7Mb)
view animation with fixed triangle (7Mb)





tri octahedra

Med
Lrg

Description :

Octahedra have their faces attached above the triangles of one
orientation and below the triangles of the other orientation. The
transformation of the triangle tiling transforms the octahedra in
their layers. At the maximum expansion the empty space forms
cuboctahedra, and these cuboctahedra close down to form a pair of
tetrahedra at the minimum expansion.
The following animations show a 2x2x2 lattice of octahedra, surounding
a single cuboctahedron space at maximum expansion.
view animation with fixed plane (3Mb)
view animation with fixed triangle (3Mb)





tri rhomb dodec

Med
Lrg

Description :

Rhombic dodecahedra have a triangular section attached to have a single
vertex above the triangles of one orientation or below the triangles of
the other orientation. The transformation of the triangle tiling
transforms the rhombic dodecahedra in
their layers.
view animation of transformation with rhombic dodecahedra (9Mb)





lattice jbug

Med
Lrg





tri torus

Med
Lrg

Description :

The transformation of the triangle tiling is mapped onto a torus.
The model was made as an aid to visualisation. It has no geometric
significance. The expansion is simulated.
view animation of torus jitterbug (4Mb)





kaleidocycle

Med
Lrg

Description :

The transformation of a triangle tiling mapped onto a torus. When there
are four triangles around the tube the result approximates a
transforming kaleidocycle. A model made with rigid triangles
would transform like this.
view animation of transforming kaleidocycle (2Mb)





squares

Med
Lrg

Description :

'Jitterbug' of a square tiling of the plane. The different colour
squares have opposite orientations.
view square tiling animation (1.5Mb)





squ cubes

Med
Lrg

Description :

Cubes have their faces attached above the squares of one
orientation or below the squares of the opposite orientation. The
transformation of the square tiling transforms the cubes in
their layers. The empty space at the maximum expansion forms
cubes, and these cubes close down to nothing at the minimum
expansion, which is just a packing of the cubes.
view animation of transformation with cubes (7Mb)





squ rhomb dodec

Med
Lrg

Description :

Rhombic dodecahedra have a square section attached to have a single
vertex above the squares of one orientation or below the squares of
the opposite orientation. The transformation of the square tiling
transforms the rhombic dodecahedra in their layers.
view animation of transformation with rhombic dodecahedra (9Mb)





squ torus

Med
Lrg

Description :

The transformation of the square tiling is mapped onto a torus.
The model was made as an aid to visualisation. It has no geometric
significance. The expansion is simulated.
view animation of torus jitterbug (3Mb)




