Pentasphere (EntityTopic, 15)
From Hi.gher. Space
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| - | {{Shape|Pentasphere| | + | <[#ontology [kind topic] [cats 5D Hypersphere]]> |
| + | {{STS Shape | ||
| + | | name=Pentasphere | ||
| + | | dim=5 | ||
| + | | elements=1, 0, 0, 0, 0 | ||
| + | | genus=0 | ||
| + | | ssc=(xyzwφ) | ||
| + | | ssc2=T5 | ||
| + | | extra={{STS Tapertope | ||
| + | | order=1, 0 | ||
| + | | notation=5 | ||
| + | | index=30 | ||
| + | }}{{STS Toratope | ||
| + | | expand=[[Pentasphere|5]] | ||
| + | | notation=(IIIII) | ||
| + | | index=9b | ||
| + | }}{{STS Bracketope | ||
| + | | index=33 | ||
| + | }}}} | ||
| - | + | == Equations == | |
| - | + | ||
*Variables: | *Variables: | ||
<blockquote>''r'' ⇒ radius of the pentasphere</blockquote> | <blockquote>''r'' ⇒ radius of the pentasphere</blockquote> | ||
| Line 14: | Line 31: | ||
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> | ||
*The [[realmic]] [[cross-section]]s (''n'') of a pentasphere are: | *The [[realmic]] [[cross-section]]s (''n'') of a pentasphere are: | ||
<blockquote>[!x,!y,!z,!w,!φ] ⇒ [[glome]] of radius (''r''cos(π''n''/2))</blockquote> | <blockquote>[!x,!y,!z,!w,!φ] ⇒ [[glome]] of radius (''r''cos(π''n''/2))</blockquote> | ||
| - | <br | + | |
| - | {{ | + | {{Pentashapes}} |
| - | {{ | + | {{Tapertope Nav|29|30|31|1<sup>1</sup>1<sup>1</sup><br>Duotrianglinder|5<br>Pentasphere|41<br>Glominder|tera}} |
| + | {{Toratope Nav B|8|9|10|((II)I)I<br>Torinder|(((II)I)I)<br>Ditorus|IIIII<br>Penteract|(IIIII)<br>Pentasphere|(II)III<br>Tesserinder|((II)III)<br>Toratesserinder|tera}} | ||
| + | {{Bracketope Nav|32|33|34|<nowiki><IIIII></nowiki><br>Aeroteron|(IIIII)<br>Pentasphere|[(II)III]<br>Tesserinder|tera}} | ||
Latest revision as of 17:38, 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 | |||||
| 32. <IIIII> Aeroteron | 33. (IIIII) Pentasphere | 34. [(II)III] Tesserinder |
| List of bracketopes | ||
