Cylspherinder (EntityTopic, 13)
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| - | {{Shape|Cylspherinder| | + | <[#ontology [kind topic] [cats 5D Tapertope Toratope Bracketope Curved]]> |
| + | {{STS Shape | ||
| + | | name=Cylspherinder | ||
| + | | dim=5 | ||
| + | | elements=2, 1, 0, 0, 0 | ||
| + | | genus=0 | ||
| + | | ssc=[(xy)(zwφ)] | ||
| + | | ssc2=T2xT3 | ||
| + | | extra={{STS Tapertope | ||
| + | | order=2, 0 | ||
| + | | notation=32 | ||
| + | | index=32 | ||
| + | }}{{STS Toratope | ||
| + | | expand=[[Cylspherinder|32]] | ||
| + | | notation=(III)(II) | ||
| + | | index=14a | ||
| + | }}{{STS Bracketope | ||
| + | | index=? | ||
| + | }}}} | ||
| + | A '''cylspherinder''' is the [[Cartesian product]] of a [[sphere]] and a [[circle]]. It is the [[expanded rotatope]] of the [[torisphere]] and [[spheritorus]]. | ||
| - | + | == Equations == | |
| - | + | ||
| - | + | ||
| - | + | ||
*Variables: | *Variables: | ||
<blockquote>''a'' ⇒ radius of the sphere<br> | <blockquote>''a'' ⇒ radius of the sphere<br> | ||
| Line 15: | Line 31: | ||
The cylspherinder will always roll when placed on a surface. If it rests on one of its [[teron|tera]], it can cover the space of a line. If it rests on its other teron, it can cover the space of a plane. | The cylspherinder will always roll when placed on a surface. If it rests on one of its [[teron|tera]], it can cover the space of a line. If it rests on its other teron, it can cover the space of a plane. | ||
| - | {{ | + | {{Pentashapes}} |
| - | {{ | + | {{Tapertope Nav|31|32|33|41<br>Glominder|32<br>Cylspherinder|311<br>Cubspherinder|tera}} |
| + | {{Toratope Nav A|13|14|15|((II)I)II<br>Cubtorinder|(((II)I)II)<br>Toracubtorinder|(III)(II)<br>Cylspherinder|((III)(II))<br>Cylspherintigroid|((II)I)(II)<br>Cyltorinder|(((II)I)(II))<br>Cyltorintigroid|tera}} | ||
| + | {{Bracketope Nav|?|?|?|?<br>?|[(II)(III)]<br>Cylspherinder|?<br>?|tera}} | ||
Latest revision as of 22:58, 11 February 2014
A cylspherinder is the Cartesian product of a sphere and a circle. It is the expanded rotatope of the torisphere and spheritorus.
Equations
- Variables:
a ⇒ radius of the sphere
b ⇒ radius of the circle
- The hypervolumes of a cylspherinder are given by:
Unknown
Rolling
The cylspherinder will always roll when placed on a surface. If it rests on one of its tera, it can cover the space of a line. If it rests on its other teron, it can cover the space of a plane.
| Notable Pentashapes | |
| Flat: | pyroteron • aeroteron • geoteron |
| Curved: | tritorus • pentasphere • glone • cylspherinder • tesserinder |
| 31. 41 Glominder | 32. 32 Cylspherinder | 33. 311 Cubspherinder |
| List of tapertopes | ||
| 13a. ((II)I)II Cubtorinder | 13b. (((II)I)II) Toracubtorinder | 14a. (III)(II) Cylspherinder | 14b. ((III)(II)) Cylspherintigroid | 15a. ((II)I)(II) Cyltorinder | 15b. (((II)I)(II)) Cyltorintigroid |
| List of toratopes | |||||
| ?. ? ? | ?. [(II)(III)] Cylspherinder | ?. ? ? |
| List of bracketopes | ||
