The Dodecahedron's Story
I, the Dodecahedron, am on vacation.

I will continue my story when I return.

Not only do I like your blog (haha I found it) but I also am OBSESSED with you secretly. Ok here we go.. I got this idea from a Tumblr spam I got once lol.. I think you like me too and you were always too shy to admit it :3 go to crushmatches(dót)com (wtf it wont let me link regular) and make an account there. Then look up the profile 'gottagetme19' (me obviously) I left body pictures.. if you can guess who I am hit me up and we'll hang soon. You need a C C but its free
Anonymous

We dodecahedra are not stupid.

what is the eqation for polyhedrons surface area

Which polyhedron?

themathkid:

platonic solids #2 by pforbinesque on Flickr.
Here is the rhombic triacontahedron, in Zome.

Here is the rhombic triacontahedron, in Zome.

The Icosidodecahedron (right) also has a dual, but it is not an Archimedean solid.  It’s one of a group of polyhedra called the Catalan Solids (duals to the Archimedeans).  This Catalan (on the left) is the rhombic triacontahedron, made of thirty congruent rhombic faces which have diagonal lengths in the golden ratio.  Kepler discovered it as well.

The Icosidodecahedron (right) also has a dual, but it is not an Archimedean solid.  It’s one of a group of polyhedra called the Catalan Solids (duals to the Archimedeans).  This Catalan (on the left) is the rhombic triacontahedron, made of thirty congruent rhombic faces which have diagonal lengths in the golden ratio.  Kepler discovered it as well.

Another view of the Icosidodecahedron, who is a bit of a show-off.  The triangular faces are hidden so that you may see the interior structure of this polyhedron.
robertlovespi:

This has “freaks” (cartoons I drew in childhood) on the pentagonal faces of an icosidodecahedron, with the triangular faces hidden.
To find the software I used, go here:  www.software3d.com/stella.php

Another view of the Icosidodecahedron, who is a bit of a show-off.  The triangular faces are hidden so that you may see the interior structure of this polyhedron.

robertlovespi:

This has “freaks” (cartoons I drew in childhood) on the pentagonal faces of an icosidodecahedron, with the triangular faces hidden.

To find the software I used, go here:  www.software3d.com/stella.php

stellaspider:

A happy Icosidodecahedron.
www.software3d.com/stella.php

stellaspider:

A happy Icosidodecahedron.

www.software3d.com/stella.php

Medium blues (my edge length, times the golden ratio) fit between the Zomeballs where medium yellows meet, outside the dodecahedron.  These medium yellows form the first of the Archimedean solids we will be looking at.
The outer blue figure is made of the twelve pentagons of mine, plus the twenty triangles of my dual.  Being a “blend” of the Dodecahedron and the Icosahedron, an appropriate name has been chosen for this Archimedean solid:  the Icosidodecahedron.
This is the first Archimedean solid I have shown you, simply because it is a type of hybrid of my dual and myself.  There are twelve others, not counting enantiomers of the same polyhedron twice, and we will see them all.

Medium blues (my edge length, times the golden ratio) fit between the Zomeballs where medium yellows meet, outside the dodecahedron.  These medium yellows form the first of the Archimedean solids we will be looking at.

The outer blue figure is made of the twelve pentagons of mine, plus the twenty triangles of my dual.  Being a “blend” of the Dodecahedron and the Icosahedron, an appropriate name has been chosen for this Archimedean solid:  the Icosidodecahedron.

This is the first Archimedean solid I have shown you, simply because it is a type of hybrid of my dual and myself.  There are twelve others, not counting enantiomers of the same polyhedron twice, and we will see them all.

Now all of the possible yellow-yellow-blue triangles (of that same type) have been built.

Now all of the possible yellow-yellow-blue triangles (of that same type) have been built.