Pentasphere (EntityTopic, 15)
From Hi.gher. Space
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<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> | ||
| - | {{ | + | {{Pentashapes}} |
{{Rotope Nav|46|47|48|IIII'<br>Tesseric pyramid|(IIIII)<br>Pentasphere|III'I<br>Cubic pyramid prism|tera}} | {{Rotope Nav|46|47|48|IIII'<br>Tesseric pyramid|(IIIII)<br>Pentasphere|III'I<br>Cubic pyramid prism|tera}} | ||
{{Bracketope Nav|111|112|113|(<xy>zwφ)<br>Narrow tricrind|(xyzwφ)<br>Pentasphere|([<xy><zw>]φ)<br>Small tesseric crind|tera}} | {{Bracketope Nav|111|112|113|(<xy>zwφ)<br>Narrow tricrind|(xyzwφ)<br>Pentasphere|([<xy><zw>]φ)<br>Small tesseric crind|tera}} | ||
Revision as of 07:10, 18 August 2007
Geometry
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 = 4π2r48-1
pentavolume = π2r58-1
- 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 |
| 111. (<xy>zwφ) Narrow tricrind | 112. (xyzwφ) Pentasphere | 113. ([<xy><zw>]φ) Small tesseric crind |
| List of bracketopes | ||
