Cosmochoron (EntityTopic, 12)
From Hi.gher. Space
The hecatonicosachoron, or 120-cell, is a 4D polytope bounded by 120 dodecahedra. Each dodecahedron lies on a ring of 10 dodecahedra along a great circle of the glome. There are 4 dodecahedra on such a ring between one dodecahedron and its antipodal dodecahedron.
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
- The hypervolumes of a hecatonicosachoron are given by:
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
- The realmic cross-sections (n) of a hecatonicosachoron are:
Unknown
Projection
http://teamikaria.com/dl/Pmyg-el9wlGbaOueUDKBuTbIo5xIx8iFlG8rLaBYljwi-z1f.gif http://teamikaria.com/dl/4TMygnHLhLXtUc0oRXtHFapu60FMLK_ig1kN2fN5GSeSdbFz.gif
Here are two perspective projections of the hecatonicosachoron into 3D. 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: | pyrochoron • aerochoron • geochoron • xylochoron • hydrochoron • cosmochoron |
Powertopes: | triangular octagoltriate • square octagoltriate • hexagonal octagoltriate • octagonal octagoltriate |
Circular: | glome • cubinder • duocylinder • spherinder • sphone • cylindrone • dicone • coninder |
Torii: | tiger • torisphere • spheritorus • torinder • ditorus |