Hydrochoron (EntityTopic, 12)
From Hi.gher. Space
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http://teamikaria.com/dl/_v_RVAMQsaCV2pHkFcBP09KGMsFA3C7nM40O3M2uT6jQQZcN.gif | http://teamikaria.com/dl/_v_RVAMQsaCV2pHkFcBP09KGMsFA3C7nM40O3M2uT6jQQZcN.gif | ||
| - | Here is a projection of the hexacosichoron. Around the central [[vertex]], which is closest to the 4D viewpoint, are 20 highlighted [[tetrahedra]], joined in the form of an [[icosahedron]]. There are two more layers visible closer to the "surface" of the 3D projection, and another three layers which are mirror images of the first three on the back of the 4D shape. | + | Here is a perspective projection of the hexacosichoron to 3D. Around the central [[vertex]], which is closest to the 4D viewpoint, are 20 highlighted [[tetrahedra]], joined in the form of an [[icosahedron]]. There are two more layers visible closer to the "surface" of the 3D projection, and another three layers which are mirror images of the first three on the back of the 4D shape. |
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Revision as of 17:32, 31 August 2008
Geometry
Equations
- Variables:
l ⇒ length of the edges of the hexacosichoron
- All points (x, y, z, w) that lie on the surcell of a hexacosichoron will satisfy the following equation:
Unknown
- The hypervolumes of a hexacosichoron are given by:
total edge length = 720l
total surface area = 300sqrt(3)l2
surcell volume = 50sqrt(2)l3
bulk = Unknown
- The realmic cross-sections (n) of a hexacosichoron are:
Unknown
Related shapes
The grand antiprism may be obtained by removing 20 vertices from the hexacosichoron lying along two mutually orthogonal rings (10 vertices each), and recomputing the convex hull.
The snub 24-cell may be obtained by removing 24 vertices from the hexacosichoron coinciding with the vertices of an inscribed 24-cell.
Projection
http://teamikaria.com/dl/_v_RVAMQsaCV2pHkFcBP09KGMsFA3C7nM40O3M2uT6jQQZcN.gif
Here is a perspective projection of the hexacosichoron to 3D. Around the central vertex, which is closest to the 4D viewpoint, are 20 highlighted tetrahedra, joined in the form of an icosahedron. There are two more layers visible closer to the "surface" of the 3D projection, and another three layers which are mirror images of the first three on the back of the 4D shape.
| 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 |
