Glome (EntityTopic, 15)
From Hi.gher. Space
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<blockquote>[!x,!y,!z,!w] ⇒ [[sphere]] of radius (''r''cos(π''n''/2))</blockquote> | <blockquote>[!x,!y,!z,!w] ⇒ [[sphere]] of radius (''r''cos(π''n''/2))</blockquote> | ||
| - | {{ | + | {{Tetrashapes}} |
{{Rotope Nav|15|16|17|III'<br>Cubic pyramid|(IIII)<br>Glome|II'I<br>Square pyramidal prism|chora}} | {{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}} | {{Bracketope Nav|39|40|41|(<xy>zw)<br>Narrow dicrind|(xyzw)<br>Glome|[<xy><zw>]<br>Small tesseract|chora}} | ||
Revision as of 20:18, 17 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))
| 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 | ||
