Glome (EntityTopic, 15)
From Hi.gher. Space
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| + | {{Shape|Glome|''No image''|4|1, 0, 0, 0|0|N/A|N/A|[[Line (object)|E]][[Circle|L]][[Sphere|L]]L|4 (x,y,z,w)|N/A|N/A|N/A|16|(xyzw)|40|pure}} | ||
| + | == Geometry == | ||
| + | === Equations === | ||
| + | *Variables: | ||
| + | <blockquote>''r'' ⇒ radius of the glome</blockquote> | ||
| + | |||
| + | *All points (''x'', ''y'', ''z'', ''w'') that lie on the [[surcell]] of a glome will satisfy the following equation: | ||
| + | <blockquote>x<sup>2</sup> + y<sup>2</sup> + z<sup>2</sup> + w<sup>2</sup> = r<sup>2</sup></blockquote> | ||
| + | |||
| + | *The [[hypervolume]]s of a glome are given by: | ||
| + | <blockquote>total edge length = 0<br> | ||
| + | total surface area = 0<br> | ||
| + | surcell volume = 2π<sup>2</sup>''r''<sup>3</sup><br> | ||
| + | bulk = 2<sup>-1</sup>π<sup>2</sup>''r''<sup>4</sup></blockquote> | ||
| + | |||
| + | *The [[realmic]] [[cross-section]]s (''n'') of a glome are: | ||
| + | <blockquote>[!x,!y,!z,!w] ⇒ [[sphere]] of radius (''r''cos(π''n''/2))</blockquote> | ||
| + | |||
| + | {{Polychora}} | ||
| + | {{Rotope Nav|15|16|17|III'<br>Cubic pyramid|(IIII)<br>Glome|II'I<br>Square pyramidal prism|chora}} | ||
| + | {{Bracketope Nav|39|40|41|(<xy>zw)<br>Narrow dicrind|(xyzw)<br>Glome|[<xy><zw>]<br>Small tesseract|chora}} | ||
Revision as of 20:07, 9 August 2007
Geometry
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))
Template:Polychora
Template:Rotope Nav
| 39. (<xy>zw) Narrow dicrind | 40. (xyzw) Glome | 41. [<xy><zw>] Small tesseract |
| List of bracketopes | ||
