Pentasphere (EntityTopic, 15)
From Hi.gher. Space
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| - | {{Shape | + | {{STS Shape |
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| name=Pentasphere | | name=Pentasphere | ||
| dim=5 | | dim=5 | ||
| elements=1, 0, 0, 0, 0 | | elements=1, 0, 0, 0, 0 | ||
| genus=0 | | genus=0 | ||
| - | |||
| ssc=(xyzwφ) | | ssc=(xyzwφ) | ||
| - | | | + | | extra={{STS Rotope |
| - | | | + | | attrib=pure |
| - | | | + | | notation=5 (xyzwφ) |
| - | }} | + | | index=47 |
| + | }}{{STS Bracketope | ||
| + | | index=148 | ||
| + | }}}} | ||
== Equations == | == Equations == | ||
Revision as of 15:55, 14 March 2008
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 |
| 147. (<xy>zwφ) Narrow tricrind | 148. (xyzwφ) Pentasphere | 149. ([<xy><zw>]φ) Narrow tesseric crind |
| List of bracketopes | ||
