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Click and drag to rotate. Ctrl + click to Zoom.
more Polyhedra (opens in new window)

This is a pentagram prism. You ignore points where the sides of the pentagram meet, so it counts as a star polygon with five sides.

Similarly, as with a normal prism, the opposite pentagram faces are joined together using squares - and again you ignore the places where the squares interesect with each other. So this is a non convex semi-regular polygon made up of squares and pentagrams.

Virtual Flower makes pentagrams and other star polygons so that the regions of the star polygon altermate between filled and empty - this lets you see inside the shape, or sometimes right through it as in this case.

Here are some more of the shapes you can make with virtual flower, including ones with star polygon faces, and self intersecting polyhedra:
More Polyhedra (opens in new window)

Then you can animate them as swirling patterns of stars and other shapes that suddenly coalesce to make the geometrical shape.
Star Spheres (opens in new window)

The wizard has the plaatonic solids, and one or two others in a short menu to get you started, but that's just the begiinning of its capabilities:

As you see, you have options to truncate it, join face centres and edge midpoints, andmake geodesic subdivsions of the faces (which can also be applied to faces with more than three sides, and with mixtures of different types of face in the same shape e.g. squares and triangles).

In the Get from File, you have a few other example shapes you can use as a starting point, such as Kepler's stellaoctangula. However what makes this option very versatile is that you can add any other shapes to that list - for instance if you save a shape from Virtual Flower itself, you can then get it from the file and then apply the various options such as to truncate it, join edge midpoints etc. This could be used e.g. to repeatedly truncate the same shape any number of times.

Also if you have VRML files of your own with geometrical shapes in them, then (depending how they are done) you may be able to import them into Virtual Flower in the same way. Techy note: it imports the first Indexed Face set it finds in your file. You can also import shapes from .wrl files yo you find on the web - but do be sure to check the author's wishes and respect copyright before doing so!

But the big list of possibilities is the one you get to from the Many other shapes entry. This uses a special feature in Virtual Flower to make a geometrical shape from its vertex pattern.

Here is one:

There the object is generated automatically from the numbers of the faces meeting at each vertex. Each vertex (corner) of the object has a square, a hexagon and an octagon meeting at it, with 4, 6 and 8 sides. So you enter the numbers 4, 6, 8 to make the shape.

Here is another one:

Here it is based on an enneagram 9/4 (a star polygon with 9 sides, and the /4 says to go around four times when you join the vertices together). This is no longer a semi regular solid. Nearly all the vertices do have an identical arrangement of faces around them, with one enneagram and two triangles meeting at each vertex, but there is one, the one at the point of the star pyramid, where nine triangles meet. Virtual flower just iterates the construction of the object from its vertex pattern as far as it can take it until all the edges join up - and sometimes as here that creates new vertices with their own patterns of faces.

This option can make many complicated non convex shapes, self intersecting ones and ones with star polygon faces, and was used to make most of the shapes on the page More Polyhedra

However, occasionally it can fit the faces together in a different way from the way you expected it to happen. This is something that needs more work, to ensure it makes the best choices when it builds up the shape. It also can't handle some star polygons which break up into several distinct shapes - it can manage the ones that break up into just two shapes like the hexagram - but not for instance, the version of the enneagram (nine sided star polygon) made up of three triangles.

Treat it as work in progress for now. But most of them do turn out as expected. All the convex regular and semi regular shapes work, and all four non convex regular shapes (the Kepler Poinsot polyhedra).

Also most of the non convex semi regular ones work too (with occasional surprises), though a few need extra parameters as hints to tell the wizard how to proceed.

Anyway for those who just want to try out some interesting shapes and maybe make some of them into star spheres - you have a big list of shapes that do work to select from. Just select the shape from the drop list and it is all set up ready for you.

Freeware / Shareware status: This feature is free. If you wish to show your appreciation, use the Donations page. You may want to you use your geometrical shapes in a shareware features of Virtual Flower - to make trees, or to make star spheres.

To read more about Virtual Flower, go on to:

Musical Geometries

To get the program, download and install Virtual Flower.

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Shapes you can make with Virtual Flower
   

Virtual Flowers and Trees
Virtual flower scenes (VRML)
Star Spheres
Geometrical Shapes
Anaglyph Garden
Higher Dimensional Shapes



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© Robert Walker 2008
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Create virtual flowers, Lissajous curves, and geometrical patterns in 3D - 3D Art
By Robert Walker
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