Torinder (EntityTopic, 11)

From Higher Dimensions Database

A torinder is the linear extension of a torus.

Equations

• Variables:

R ⇒ major radius of the torinder
r ⇒ minor radius of the torinder
h ⇒ height of the torinder

• All points (x, y, z, w) that lie on the surcell of a torinder will satisfy the following equation:

h ≥ |w|
r² = (sqrt(x² + y²) - R)² + z²

• The parametric equations are:

x = (R + r cos(θ)) cos(Φ)
y = (R + r cos(θ)) sin(Φ)
z = r sin(θ)
w = w

• The hypervolumes of a torinder are given by:

surface area of margin = 8π²Rr
surcell volume = 4πRr(πr + h)
bulk = 2π²Rr²h

• The realmic cross-sections (n) of a torinder are:

Unknown

Notable Tetrashapes
Regular:	pyrochoron • aerochoron • geochoron • xylochoron • hydrochoron • cosmochoron
Powertopes:	triangular octagoltriate • square octagoltriate • hexagonal octagoltriate • octagonal octagoltriate
Circular:	glome • cubinder • duocylinder • spherinder • sphone • dicone • coninder
Torii:	tiger • toraspherinder • toracubinder • torinder • ditorus

7a. (III)I Spherinder	7b. ((III)I) Toraspherinder	8a. ((II)I)I Torinder	8b. (((II)I)I) Ditorus	9a. IIIII Penteract	9b. (IIIII) Pentasphere
List of toratopes