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Here are models of the five Platonic solids made from the  four smallest symmetrical tetrahedra (A, B, Icosa, and Dodeca Quanta) that will build them all:
tetrahedron - 24 A Quanta
hexahedron (cube) - 48 A Quanta + 24 B Quanta
octahedron - 48 A Quanta + 48 B Quanta
icosahedron - 120 Icosa Quanta
dodecahedron - 120 Dodeca Quanta

The rhombic dodecahedron can also be built with 96 A Quanta + 48 B Quanta, or two cubes divided into quarters turned inside out.

The A and B Quanta have the same volume.  I have not determined whether the Icosa Quanta and Dodeca Quanta share that characteristic.

The scale used in these patterns is based upon the one right triangle which is common between all the Quanta, a triangle of 90º, 54º 44', and 35º 16'.

Materials:
colored acetate and PVC
clear tape
ceramic magnets
colored cardstock
miracle glue

Update:  Now with video.

Prepared these models for the Synergetics Symposium at RI School of Design over a year ago.  These models all have magnets at the center of each face.  Next edition, if I ever get the inclination to build it, should be wire framework models with ball magnets at each vertex, which I think is more realistic.

If you are interested in these kind of geometrics, you should be aware of the Synergetics Collaborative http://www.synergeticscollaborative.org/

Dancing the Cube in Jamaica

Six Right Triangles

Pandora's Box

Originally posted to gmoke on Sun Nov 28, 2010 at 06:37 PM PST.

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Comment Preferences

  •  Tip Jar (18+ / 0-)

    Solar is civil defense. Video of my small scale solar experiments at solarray.

    by gmoke on Sun Nov 28, 2010 at 06:37:48 PM PST

  •  Based on the information you've given -- (3+ / 0-)
    Recommended by:
    gmoke, pico, Lujane
    The A and B Quanta have the same volume.  I have not determined whether the Icosa Quanta and Dodeca Quanta share that characteristic.

    The volume of a unit icosahedron (e.g., sides = 1 unit) is (15 + 5sqrt(5))12 (approximately 2.18).

    The volume of a unit dodecahedron is (15 + 7sqrt(5))/4 (approximately 7.66).  

    Since each is made of 120 quanta, then -- based on the information you've given, the quanta have different volumes /if the side length of the finished polyhedron is kept fixed.  

    However, based on your assertion that the A quanta and B quanta have the same volume, that's not the standard you're using (the side lengths of your tetrahedron and cube are different).

    I represent the Mondays Are Too Damn Long Party.

    by osterizer on Sun Nov 28, 2010 at 07:03:29 PM PST

    •  wooooo! (2+ / 0-)
      Recommended by:
      gmoke, Lujane
      The division sign in my first fraction was interpreted as a "start italics" forward slash -- not what I had intended.  

      Sorry about that.

      I represent the Mondays Are Too Damn Long Party.

      by osterizer on Sun Nov 28, 2010 at 07:04:56 PM PST

      [ Parent ]

    •  Volumes of Quanta (4+ / 0-)
      Recommended by:
      osterizer, Blueiz, pico, Lujane

      That the A and B Quanta have the same volume comes from R Buckminster Fuller's Synergetics.  I don't do mathematics.  I sometimes build models.

      Yep, you're right that the Icosa and Dodeca Quanta can't have the same volumes.

      Fuller also described a C, D, and other Quanta, including an S Quanta which is the difference between an Octahedron and an Icosahedron.

      Solar is civil defense. Video of my small scale solar experiments at solarray.

      by gmoke on Sun Nov 28, 2010 at 07:50:40 PM PST

      [ Parent ]

  •  With Maybe Just Triple the Word Count (2+ / 0-)
    Recommended by:
    gmoke, Lujane

    maybe 5-10x more of us would be able to enjoy this.

    But maybe I'm the sole member of the set that loves math in principle but sucks at it. Burns the hell out of me that I can't be fluent in this area.

    We are called to speak for the weak, for the voiceless, for victims of our nation and for those it calls enemy.... --ML King "Beyond Vietnam"

    by Gooserock on Sun Nov 28, 2010 at 07:41:13 PM PST

    •  Word Counts (1+ / 0-)
      Recommended by:
      Remembering Jello

      The pictures tell the story.  If I had a scan of the nets, the four triangles that make up each of these symmetrical tetrahedral (four-sided) figures, all the visual information would be there and I wouldn't have to use any words at all.

      Nevertheless, thanks for reading.

      Solar is civil defense. Video of my small scale solar experiments at solarray.

      by gmoke on Sun Nov 28, 2010 at 07:56:26 PM PST

      [ Parent ]

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