# Crind (EntityTopic, 10)

(Redirected from Bracketope 9)

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 + yx + z = r
-- or --
x + zx + 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
total edge length = 4πsqrt(2)r
surface area = Unknown
volume = πr3
[!x,!y] ⇒ circle [!z] ⇒ square
[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