Pentasphere (EntityTopic, 15)
From Hi.gher. Space
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total surface area = 0<br> | total surface area = 0<br> | ||
total surcell volume = 0<br> | total surcell volume = 0<br> | ||
| - | surteron bulk = | + | surteron bulk = {{Over|π<sup>2</sup>|2}} {{DotHV|4|r}}<br> |
| - | pentavolume = π<sup>2</sup>r | + | pentavolume = {{Over|π<sup>2</sup>|8}} {{DotHV|5|r}} |
</blockquote> | </blockquote> | ||
Revision as of 16:00, 18 November 2011
Equations
- Variables:
r ⇒ radius of the pentasphere
- All points (x, y, z, w, φ) that lie on the surteron of a pentasphere will satisfy the following equation:
x2 + y2 + z2 + w2 + φ2 = r2
- The hypervolumes of a pentasphere are given by:
total edge length = 0
total surface area = 0
total surcell volume = 0
surteron bulk = π2∕2 · r4
pentavolume = π2∕8 · r5
- The realmic cross-sections (n) of a pentasphere are:
[!x,!y,!z,!w,!φ] ⇒ glome of radius (rcos(πn/2))
| Notable Pentashapes | |
| Flat: | pyroteron • aeroteron • geoteron |
| Curved: | tritorus • pentasphere • glone • cylspherinder • tesserinder |
| 29. 1111 Duotrianglinder | 30. 5 Pentasphere | 31. 41 Glominder |
| List of tapertopes | ||
| 8a. ((II)I)I Torinder | 8b. (((II)I)I) Ditorus | 9a. IIIII Penteract | 9b. (IIIII) Pentasphere | 10a. (II)III Tesserinder | 10b. ((II)III) Toratesserinder |
| List of toratopes | |||||
| 147. (<xy>zwφ) Narrow tricrind | 148. (xyzwφ) Pentasphere | 149. ([<xy><zw>]φ) Narrow tesseric crind |
| List of bracketopes | ||
