Crind (EntityTopic, 10)

From Higher Dimensions Database


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
Unknown
[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: tetrahedroncubeoctahedrondodecahedronicosahedron
Direct truncates: tetrahedral truncatecubic truncateoctahedral truncatedodecahedral truncateicosahedral truncate
Mesotruncates: stauromesohedronstauroperihedronstauropantohedronrhodomesohedronrhodoperihedronrhodopantohedron
Snubs: snub staurohedronsnub rhodohedron
Curved: spheretoruscylinderconefrustumcrind


8. <(II)I>
Bicone
9. ([II]I)
Crind
10. [IIII]
Geochoron
List of bracketopes