Pentasphere (EntityTopic, 15)

(Difference between revisions)

Revision as of 20:00, 25 November 2009

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 = 4π²r⁴8^-1
pentavolume = π²r⁵8^-1

[!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

@@ Line 6: / Line 6: @@
 | ssc=(xyzwφ)
 | ssc2=T5
-| extra={{STS Rotope
+| extra={{STS Tapertope
-| attrib=pure
+| order=1, 0
-| notation=5 (xyzwφ)
+| notation=5
-| index=47
+| index=30
+}}{{STS Toratope
+| holeseq=[0, 0, 0, 1]
+| notation=(IIIII)
+| index=9b
 }}{{STS Bracketope
 | index=148
@@ Line 34: / Line 38: @@
 {{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|chora}}
+{{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|chora}}
 {{Bracketope Nav|147|148|149|(<xy>zwφ)<br>Narrow tricrind|(xyzwφ)<br>Pentasphere|([<xy><zw>]φ)<br>Narrow tesseric crind|tera}}