© 2014 Dead Homer

Hinged Plate-Polygons

partcount-segment-4 partcount-total-96 shape-polyeder-12 shape-polyeder-20 shape-polyeder-4 shape-polyeder-6 shape-sphere size-10s-10s-10s

Can be used to create the Platonic Solids – see these examples:

Octahedron, Tetrahedron, Cube

Dead Homer ( 2014-11-07, flickr.com )

For completeness, the remaining Platonic solids

Icosahedron

Dead Homer ( 2014-11-07, flickr.com )

First built in 2000, with the old finger hinges. And then I went crazy a built LOTS of polyhedra.

Dodecahedron

Dead Homer ( 2014-11-07, flickr.com )

Dual to the icosahedron, and therefore built with exactly the same parts

The same principle can also be used to create any thinkable shape in 3D space. Here are some more examples:

Rhombic Triacontahedron

Joe Miller ( 2015-01-11, flickr.com )

You may have seen Dead Homer’s version in the Lego Movie. Although I designed this a long time ago, it is essentially the *exact* same design

Polyhedral Ornaments

Chamberlain Fong ( 2021-07-26, polyhedonistic.blogspot.com )

For our paper on LEGO polyhedra, I built several truncated octahedron models.

Polyhedral Approximations of the Sphere in LEGO®

Jin Yamauchi & Chamberlain Fong ( 2021-01-01, archive.bridgesmathart.org )

We present our attempts at modeling the sphere using LEGO® parts. We approach this task by approximating various well-known polyhedral shapes and assessing their resemblance to the sphere.

Instead of plates, the polygons can also be made of other parts – like locking hinge pieces:

Lunar Oasis

Miro Dudas ( 2015-07-03, flickr.com )

Dome is a truncated icosahedron (classic soccer ball pattern of hexagons and pentagons).

Swiss Cheese Dome

Miro Dudas ( 2015-11-15, flickr.com )

Scaled up the brick hinge dome by double the dimensions. 280 brick hinges used to make 20 hexagons and 6 pentagons.