Crind (EntityTopic, 10)
From Hi.gher. Space
(Difference between revisions)
m (K6.4 upgrade: img -> embed) |
Username5243 (Talk | contribs) |
||
Line 9: | Line 9: | ||
| extra={{STS Bracketope | | extra={{STS Bracketope | ||
| index=9 | | index=9 | ||
+ | | notation=([II]I) | ||
}}}} | }}}} | ||
Line 36: | Line 37: | ||
*The [[planar]] [[cross-section]]s (''n'') of a crind are: | *The [[planar]] [[cross-section]]s (''n'') of a crind are: | ||
- | <blockquote> | + | <blockquote>[!x,!y] ⇒ circle |
+ | [!z] ⇒ square | ||
+ | </blockquote> | ||
*The [[radial slice]]s ''θ'' of a crind are: | *The [[radial slice]]s ''θ'' of a crind are: |
Latest revision as of 02:40, 26 March 2017
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.
Its maximal and minimal compressions are an irregular octahedron and a line segment respectively.
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:
[!x,!y] ⇒ circle [!z] ⇒ square
- The radial slices θ of a crind are:
[x:xy,x:xz] ⇒ ellipse with major radius rsin(45° + (θ % 90°)√2 and minor radius r
[y:xy,y:yz,z:xz,z:yz] ⇒ "circle with ends cut" of unknown proportions
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 |
8. <(II)I> Bicone | 9. ([II]I) Crind | 10. [IIII] Geochoron |
List of bracketopes |