Various shapes - many are star polyhedra

Made with Virtual Flower

A star polygon is a shape like that five pointed star you can draw with a single continuous line. You can see one in this Pentagrammatic prism.

You ignore points where lines intersect - so this is a star polygon with five sides. If you trace round the sides of the polygon, you go its centre twice. With some other star polygons you go round more than twice. Virtual Flower makes these shapes so that the regions of the star polygon alternate between filled and empty - this let's you see into the centre of some of them, and look right through other ones such as this one here.

You can also join faces together in such a way that as you follow the faces round a vertex edge to edge, you go round two or more times, and so can fit more faces round each vertex. You ignore the places where the faces intersect. When you do this with pentagons (polygons with five sides), you get the Great dodecahedron, which is made of pentagons meeting five to a vertex instead of the usual three. Try turning it around (click and drag on the picture) - can you see that it is made of intersecting pentagons?

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Many of the shapes on this page are uniform - which means the pattern of polygons is the same around every vertex. For information about these shapes visit George Hart's polyhedron encyclopedia, particularly his section on Uniform polyhedra. You can make all these shapes with my Virtual Flower program, and many more ones too.

cubitruncated_cuboctahedron.htm Study

Dodecadodecahedron Study

Dodecagrammatic star pyramid Study

Great cubicuboctahedron Study

Great dodecahedron Study

Great dodecicosidodecahedron Study

Great dodekic icosidodecahedron Study

Great icosahedron Study

Great retrosnub icosidodecahedron Study

Great snub icosidisdodecahedron Study

Great stellated dodecahedron Study

Great stellated truncated dodecahedron Study