Six Degrees of Freedom

 

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Six Degrees of Freedom is a program that generates symmetrical patterns from perspective renderings of overlapping and rotating polyhedra. These wireframe forms, built and animated with code, endlessly rotate in shared digital space.

Six Degrees of Freedom was exhibited at the gallery, Chambers @ 916, November and December, 2012.

Girih Polyhedra, Heptakaidecahedra with Elongated Hexagon

Girih Polyhedra, Chalice Wireframe

Pentagonal Orthobirotunda Pattern

Girih patterns are decorative Islamic designs in which star shapes and polygons are connected with interlacing straight lines. Girih (Persian for “knot”) can be painstakingly created with a straightedge and compass. About nine hundred years ago Islamic architects developed an ingenious method for generating girih patterns simply with tiles. The girih tiles are five decorated polygons used to create girih patterns systematically without the need for complex drafting. We can extend the girih system into three dimensions by applying the concept to the faces of polyhedra.

Here are twelve pentagonal orthobirotundi, with girih patterns.

Girih Icosidodecahedron and Pentagonal Orthobirotunda

These two girih polyhedra are a 32-faced icosidodecahedron and the related pentagonal orthobirotunda. They each include 12 pentagon and 20 triangle faces. The pentagons are decorated with the girih tile pattern. A similar pattern continues across the equilateral triangles.

Icosidodecahedron Wireframe Girih Pattern

Icosidodecahedron with Girih Pattern

Icosidodecahedron

Pentagonal Orthobirotunda Wireframe Girih Pattern

Pentagonal Orthobirotunda with Girih Pattern

Pentagonal Orthobirotunda

Chalice: Concave Girih Polyhedra with Decagons and Pentagons

These girih polyhedra have 32 faces. They include 2 decagon and 10 pentagon faces, as well as triangles. The decagon and pentagon are decorated with the girih tile pattern. A similar pattern continues across the triangles. The triangles are equilateral.

These polyhedra are related to an icosidodecahedron and pentagonal orthobirotunda. You can split an icosidodecahedron in half (making two pentagonal rotunda) and reattached the halves at pentagons to create the chalice.

Chalice Wireframe Girih Pattern

Girih Polyhedra with Decagons and Elongated Hexagons

These girih polyhedra have 32 faces. They're related to the quasiregular polyhedron, the icosidodecahedron. They include 2 decagon and 10 elongated hexagon faces, as well as triangles. The decagon and elongated hexagon are decorated with the girih tile pattern. A similar pattern continues across the triangles.

 32 Faces with Girih Pattern

32 faces

 32 Faces with Wireframe Girih Pattern