Cosmochoron (EntityTopic, 12)

From Hi.gher. Space

Revision as of 04:29, 30 August 2008 by Hayate (Talk | contribs)


Geometry

Equations

  • Variables:
l ⇒ length of the edges of the hecatonicosachoron
  • All points (x, y, z, w) that lie on the surcell of a hecatonicosachoron will satisfy the following equation:
Unknown
total edge length = 1200l
total surface area = 180l2sqrt(25+10sqrt(5))
surcell volume = 300l3(tan(3π10-1))2(tan(sin-1(2sin(π5-1))-1))
bulk = Unknown
Unknown

Projection

http://teamikaria.com/dl/Pmyg-el9wlGbaOueUDKBuTbIo5xIx8iFlG8rLaBYljwi-z1f.gif http://teamikaria.com/dl/4TMygnHLhLXtUc0oRXtHFapu60FMLK_ig1kN2fN5GSeSdbFz.gif

Here are two projections of the hecatonicosachoron. The highlighted center cell is closest to the 4D viewpoint. It is surrounded by 12 dodecahedra in a second layer. The right-hand image also shows the third layer of 47 dodecahedra. There are three more layers which are mirror images of the first three and cannot be seen as they are on the 4D "back" of the shape. Note that only the projection is rotating; the 4D shape itself is not.




Notable Tetrashapes
Regular: pyrochoronaerochorongeochoronxylochoronhydrochoroncosmochoron
Powertopes: triangular octagoltriatesquare octagoltriatehexagonal octagoltriateoctagonal octagoltriate
Circular: glomecubinderduocylinderspherindersphonecylindronediconeconinder
Torii: tigertorispherespheritorustorinderditorus