Hydrochoron (EntityTopic, 12)

From Hi.gher. Space

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 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.