Polyhedral Solids (perhaps that's redundant, but it gets the point across.

Dedicated to Archimedes.

There are 3 classes of sorta-regular solids (polyhedrons) ...
1.- all faces are the same regular polygon -- there are only 5 of these, see at ...
       http://mathforum.org/alejandre/applet.polyhedra.html
2.- all faces are a regular polygon (but not the same one) there are a LOT of these -- like domes and soccer balls
3.- all faces are the same polygon (but not necessarily regular ones)
See more at ...
   http://illuminations.nctm.org/ActivityDetail.aspx?ID=125
There are some cut outs at ...
   http://isotropic.org/polyhedra/ (the most familiar 18 of Types 1 & 2)
   http://www.senteacher.org/wk/3dshape.php
    (but only 4 of the 5 possible type 1's.)
There are some very good examples( 30 of types 1, 2, & 3)
    -- which even can EVEN BE ROTATED in 3-D at ...
   http://jcrystal.com/steffenweber/
   http://jcrystal.com/steffenweber/POLYHEDRA/
   http://jcrystal.com/steffenweber/POLYHEDRA/p_00.html
See also --
   http://mathforum.org/mathtools/cell/m6,8.12.1,ALL,ALL/
   http://www.fi.uu.nl/toepassingen/00297/toepassing_wisweb.en.html
   http://web.aanet.com.au/robertw/Stella.html
   http://web.aanet.com.au/robertw/PolyNav/PolyNavigator.html
   http://www.google.com/search?hl=en&q=polyhedrons+cutouts
   http://www.crystalinks.com/archimedes.html
   http://www.georgehart.com/pavilion.html
   http://www.georgehart.com/virtual-polyhedra/zometool.html
   http://www.georgehart.com/virtual-polyhedra/synestructics.html
   http://www.georgehart.com/virtual-polyhedra/naming.html
   http://en.wikipedia.org/wiki/Polyhedron

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My interest was recently re-kindled when a classmate sent me an E-Mail with the subject of
      “The Beauty of Mathematics”
    which linked to ...
   http://www.youtube.com/watch_popup?v=h60r2HPsiuM
   http://www.youtube.com/watch_popup?v=h60r2HPsiuM&feature=youtube_gdata_player
      which starts w/ 12345x8+5=98765 etc etc and ends with an inspirational message,
      after which it then offers a LOT of miscellaneous random choices one of which leads to
      a linked set of videos under the title of “The Beauty of Mathematics - You Tube”.
    Following all of the links is very interesting, but the address-line/URL never changes,
       so I had NO way to get back to some of the heart of the material.
By trail and error I finally got to ...
           http://www.youtube.com/watch?v=ZOqg5bPZ0HE
    which is a lecturer with neat wall hangings.
    After which there is another set, one of which is
          http://www.youtube.com/watch?v=f81ZEVO6Btw

Then, too there are still more interesting WebSites to explore, as at ...
         https://www.google.com/#q=%22beauty+of+mathematics%22
         http://videos.sacredgeometryweb.com/category/shape/platonic-solids/
         http://videos.sacredgeometryweb.com/snub-cuboctahedron/
         https://www.google.com/#q=flower+of+life+masonic+secrets+sacred+geometery

    http://peda.com/poly
    http://mathsci.kaist.ac.kr/~drake/tes.html
http://michael-hogg.co.uk

------------
http://www.world-mysteries.com/sar_sage1.htm
http://en.wikipedia.org/wiki/Fibonacci_number
http://oeis.org/A001622
http://video.mit.edu/watch/metamorphosis-of-the-cube-12077/
http://mit.tv/NN5mLe

https://www.google.com/#psj=1&q=vertices+edges+faces
http://www.ezschool.com/Math/Shapes/ws12.html

Other terms and concepts ---
# of vertices, edges, faces   FVE   EFV FEV VEF
dual duality
prism anti-prism
prism or antiprism.
truncated   snub
star stellated
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N.B.::
1. The majority of these solids can be morphed into related but different geometries by ...
                  [ see at   http://en.wikipedia.org/wiki/Truncated_polyhedron ]
    a1 .- filing off the vertices to increase the number of faces by the number of vertices;
               then the result is said to be a TRUNCATED solid.
    a2 .- when the new lengthening/emerging edges equal the shortening/disappearing edges;
               then the result is said to be a UNIFORM TRUNCATED solid.
    a3 .- continued filing will eventually result in the new faces meeting each other
               as some of the shortened edges reach a length of zero;
               then the result is said to be a RECTIFIED TRUNCATED solid.

    b1 .- building pyramids on the faces to increase the number of faces
               by the twice the number of edges, while original faces disappear
    b2 .- continued heightening the pyramids will increase the length of the new edges;
                for n<6 sides/face of the original, the edge length will get to be equal to the orig edges.
                for n>6 sides/face of the original, the edge length will always be greater than the orig edges.
    b3 .- continued heightening the pyramids will eventually result in the new faces
                becoming co-planar, which will cut the total number of faces in half
                and make all of the orig edges disappear.
    b4 .- in some cases b2 & b3 may occur at the same height.
    b5 .- continuing beyond b3 will violate the requirement of being convex.

2. There are 43380 distinct nets for the icosahedron, the same number as for the dodecahedron .
          [ as see at https://www.google.com/#q=43380+polyhedron ]