Escher’s Geometric Universe

M. C. Esher’s “Stars“.  It’s a world of sharp-edged shapes.  Mathematicians love it, because it contains so many polyhedra (many sided, straight edged shapes).  Non-mathematician find it fascinating because Escher used mathematical constructs and created a universe full of imagination from them.

You can enjoy yourself picking out the different shapes, shapes like the Dodecahedron:

Dodecahedron by Jovan Cormac

Dodecahedron, image created by Jovan Cormac

Or the Icosahedron

Icosahedron, image created by Jovan Cormac

Icosahedron, image created by Jovan Cormac

Or the Octahedron:

Octahedron, image created by Jovan Cormac

Octahedron, image created by Jovan Cormac

Or the Stellated Icosahedron:

Stellated Icosahedron, image by Maksim

Stellated Icosahedron, image by Maksim

Or the Rhombicub Octahedron:

Rhombicub Octahedron, image adapted by Cyp

Rhombicub Octahedron, image adapted by Cyp

There are cubes combined with other shapes.  Some shapes are shown as solid, some with three dimensional outlines.  In the centre, looming large, and occupied by two chameleons, is the Stellated Rhombic  Dodecahedron.

Stellation of Rhombic Dodecahedron, by Ted-43

Stellation of Rhombic Dodecahedron, by Ted-43

There are so many ways of seeing these complex shapes.  Watching a dodecahedron being created using origami gives us another way of visualizing it.

Have fun.  Explore.  Enjoy.  Escher did.

Images:

M. C. Escher, Stars
http://www.mcescher.com/Gallery/back-bmp/LW359C.jpg

Octahedron, Dodecaheron, and Icosahedron images created by Jovan Cormac and distributed under Creative Commons Attribution/Share Alike 3.0 Unported license.

Stellated icosahedron image created by Maksim and distributed under Creative Commons Attribution/Share Alike 3.0 Unported license.

Rhombicub Octahedron adapted by Cyp using POV-Ray and distributed under Creative Commons Attribution/Share Alike 3.0 Unported license.

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