Pentasphere (EntityTopic, 15)

(Difference between revisions)

Latest revision as of 17:38, 18 November 2011

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

total edge length = 0
total surface area = 0
total surcell volume = 0
surteron bulk = ^π²∕₂ · r⁴
pentavolume = ^π²∕₈ · r⁵

[!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

@@ Line 1: / Line 1: @@
-{{Shape
+<[#ontology [kind topic] [cats 5D Hypersphere]]>
-| attrib=pure
+{{STS Shape
 | name=Pentasphere
 | dim=5
 | elements=1, 0, 0, 0, 0
 | genus=0
-| 20=SSC
 | ssc=(xyzwφ)
-| rns=5 (xyzwφ)
+| ssc2=T5
-| rot_i=47
+| extra={{STS Tapertope
-| bra_i=148
+| order=1, 0
-}}
+| notation=5
+| index=30
+}}{{STS Toratope
+| expand=[[Pentasphere|5]]
+| notation=(IIIII)
+| index=9b
+}}{{STS Bracketope
+| index=33
+}}}}
 == Equations ==
@@ Line 24: / Line 31: @@
 total surface area = 0<br>
 total surcell volume = 0<br>
-surteron bulk = 4π<sup>2</sup>r<sup>4</sup>8<sup>-1</sup><br>
+surteron bulk = {{Over|π<sup>2</sup>|2}} {{DotHV|4|r}}<br>
-pentavolume = π<sup>2</sup>r<sup>5</sup>8<sup>-1</sup>
+pentavolume = {{Over|π<sup>2</sup>|8}} {{DotHV|5|r}}
 </blockquote>
@@ Line 32: / Line 39: @@
 {{Pentashapes}}
-{{Rotope Nav|46|47|48|IIII'<br>Tesseric pyramid|(IIIII)<br>Pentasphere|III'I<br>Cubic pyramid prism|tera}}
+{{Tapertope Nav|29|30|31|1<sup>1</sup>1<sup>1</sup><br>Duotrianglinder|5<br>Pentasphere|41<br>Glominder|tera}}
-{{Bracketope Nav|147|148|149|(<xy>zwφ)<br>Narrow tricrind|(xyzwφ)<br>Pentasphere|([<xy><zw>]φ)<br>Narrow tesseric crind|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}}