Tetrahedra and Icosahedra in the Arizona Desert



Click to enlarge Click to enlarge

Stage-2 Sierpinski Tetrahedron sitting in an Acacia smallii tree (originally from Mexico) at the Desert Botanical Gardens in Spring 2001. I lost this wonderful bright yellow-green tetrahedron when out taking pictures one day and haven't been able to remix the paint (it was a mixture of several mixtures). It really seemed to capture the greens in a lot of plants, especially the bright greens of springtime when new leaves are coming on. To color drawing, click to enlarge,then print on "Landscape" setting, found under "Page Setup" or "Print Options." 


 
 
 

Click to enlarge Click to enlarge

Looking at this Acacia karoo tree, native to Africa, it seems like little birds would really like sitting in it. Look at those thorns!!! Now look at the icosahedron. It has a special shading on the faces. This shading pattern comes from Anna Rodenhausen, a friend and mathematician from Bremen, and is specifically related to the interior structure of an intersection of three golden rectangles. Maybe she will write something to insert here to explain it. It was Anna who opened my eyes to the beauty of the icosahedron. 

Maybe when using crayons or colored pencils on the drawing, the tinting of the faces of the icosahedron could be included. A little bird sitting protected in all those thorns might be a nice addition, too.


 
 
 

Click to enlarge Click to enlarge

Stage-2 Sierpinski Tetrahedron sitting in a Little-leaf Palo Verde (Cercidium microphyllum)at the Desert Botanical Gardens. My favorite part is the angles that the tetrahedron makes with the branches.


 
 
 

Click to enlarge Click to enlarge

This plant is an Agave sp. Taken at the Desert Botanical Gardens in Phoenix, Arizona in Summer 2001. The tetrahedrons are painted in Phthalo Blue.

Notice in the drawing, the bottom portion of the large tetrahedron is missing quite a bit of detail. It also looks as though I completely left out the top-left portion of the photograph in the drawing. This detail can be added, by you, if you print the drawing out.


 
 
 

Click to enlarge Click to enlarge

Stage-2 constructible Sierpinski Tetrahedron with a beautiful, thorny desert plant, Crown of Thorns (Euphorbia milliiv. 'Splendens'), native to Mexico, at the Desert Botanical Gardens in Phoenix, Arizona.


 
 
 

Click to enlarge Click to enlarge

Taken at the Desert Botanical Gardens. I've always liked barrel cacti. They are pretty and don't get the ground full of stickers. The cacti in the background that look like upside-down parabolas are called Octopus Cactus (Stenocereus alamosensis). The stage-3 Sierpinski looks good with the cacti, doesn't it?



 

Frequently Asked Questions

The contents of this web page are © Copyright Gayla Chandler.
Permission must be sought for all but personal use for study or enjoyment.