Crind (EntityTopic, 10)
From Hi.gher. Space
(Difference between revisions)
m (fix) |
m (add) |
||
| Line 1: | Line 1: | ||
| - | {{Shape|Crind|http://img46.imageshack.us/img46/779/crind1pt.png|3|4, 4, 2|0|N/A|N/A|[[Line (object)|E]][[Circle|L]][[Cylinder|E]]&E[[Square|E]]L|N/A|[[Square]], edge 1|N/A|N/A|N/A}} | + | {{Shape|Crind|http://img46.imageshack.us/img46/779/crind1pt.png|3|4, 4, 2|0|N/A|N/A|[[Line (object)|E]][[Circle|L]][[Cylinder|E]]&E[[Square|E]]L|N/A|[[Square]], edge 1|N/A|N/A|N/A|([xy]z)|11}} |
== Geometry == | == Geometry == | ||
A '''crind''' is the [[intersect]]ion of two perpendicular [[cylinder]]s. Due to momentum it will behave similarly to a [[duocylinder]] if left to roll on a [[surface]]. However, unlike a duocylinder, a crind can be stopped and then rolled in a different direction without needing to [[rotate]] it. | A '''crind''' is the [[intersect]]ion of two perpendicular [[cylinder]]s. Due to momentum it will behave similarly to a [[duocylinder]] if left to roll on a [[surface]]. However, unlike a duocylinder, a crind can be stopped and then rolled in a different direction without needing to [[rotate]] it. | ||
Revision as of 13:40, 18 June 2007
Geometry
A crind is the intersection of two perpendicular cylinders. Due to momentum it will behave similarly to a duocylinder if left to roll on a surface. However, unlike a duocylinder, a crind can be stopped and then rolled in a different direction without needing to rotate it.
The crind is also one of the few curved polyhedra that satisfies Euler's F + V = E + 2.
Equations
- Assumption: Crind is centered at the origin.
- Variables:
r ⇒ radius of crind
- All points (x, y, z) that lie on the surface of a crind will satisfy the following equations:
x + y ≤ x + z = r
-- or --
x + z ≤ x + y = r
- All points (x, y, z) that lie on the edges of a crind will satisfy the following equation:
x + y = x + z = r
- The hypervolumes of a crind are given by:
total edge length = 4πsqrt(2)r
surface area = Unknown
volume = πr3
- The planar cross-sections (n) of a crind are:
Unknown
| Notable Trishapes | |
| Regular: | tetrahedron • cube • octahedron • dodecahedron • icosahedron |
| Direct truncates: | tetrahedral truncate • cubic truncate • octahedral truncate • dodecahedral truncate • icosahedral truncate |
| Mesotruncates: | stauromesohedron • stauroperihedron • stauropantohedron • rhodomesohedron • rhodoperihedron • rhodopantohedron |
| Snubs: | snub staurohedron • snub rhodohedron |
| Curved: | sphere • torus • cylinder • cone • frustum • crind |
