Glome (EntityTopic, 15)
From Hi.gher. Space
(Difference between revisions)
m (Remove extraneous space) |
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| Line 5: | Line 5: | ||
| genus=0 | | genus=0 | ||
| ssc=(xyzw) | | ssc=(xyzw) | ||
| + | | ssc2=T4 | ||
| pv_circle=1 | | pv_circle=1 | ||
| pv_square=<sup>π<sup>2</sup></sup>⁄<sub>32</sub> ≈ 0.3084 | | pv_square=<sup>π<sup>2</sup></sup>⁄<sub>32</sub> ≈ 0.3084 | ||
Revision as of 16:24, 28 October 2008
The glome, also known as the 3-sphere, is the 4-dimensional equivalent of a 3D sphere. It consists of a curved 3-manifold that forms circular intersections with planes, and spherical intersections with hyperplanes. The set of points midway between two antipodal points form a sphere, hence one may think of the glome as having a spherical "equator".
Its projection to 3-space is a sphere—or, more properly, a ball: the image of its bounding manifold covers all points in a ball twice, once for each hemi-glome.
Equations
- Variables:
r ⇒ radius of the glome
- All points (x, y, z, w) that lie on the surcell of a glome will satisfy the following equation:
x2 + y2 + z2 + w2 = r2
- The hypervolumes of a glome are given by:
total edge length = 0
total surface area = 0
surcell volume = 2π2r3
bulk = 2-1π2r4
- The realmic cross-sections (n) of a glome are:
[!x,!y,!z,!w] ⇒ sphere of radius (rcos(πn/2))
| 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 |
| 39. (<xy>zw) Narrow dicrind | 40. (xyzw) Glome | 41. [<xy><zw>] Small tesseract |
| List of bracketopes | ||
