Crind (EntityTopic, 10)

From Hi.gher. Space

Revision as of 17:36, 28 October 2008

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:

Unknown

• 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