Surteron bulk

The surteron bulk of a shape is the total bulk of all of that shapes tera. It can be considered to be the total extent of all of the shape's 4-subfacets in four-dimensional space. The surteron bulk of a polychoron is typically just called its bulk.

Objects of three dimensions and below have a surteron bulk of zero; it is a property only held by four dimensional and greater shapes.

A surteron bulk has dimensions of [length]⁴.

Integral Formulae

The surteron bulk can be determined by integrating the constant function over the bulk of a shape as $\iiiint\limits_D \,dx\,dy\,dz\,dw$. This allows short formulae for the surteron bulk of many four-dimensional shapes to be derived, especially when the integral is transformed into the correct coordinate system.

Surteron Bulk Formulae

4 Dimensions

Shape	Bulk Formula	Variables
Tesseract	$abcd$	a, b, c, d = edge lengths
Cubinder	$\frac{\pi}{4} ab d^2$	a, b = edge lengths, d = diameter of disc
Duocylinder	$\frac{\pi^2}{16} {d_{1}}^2 {d_{2}}^2$	d1, d2 = diameters of discs
Spherinder	$\frac{\pi}{6} a {d}^3$	a = edge length, d = diameter of ball
Gongol	$\frac{\pi^2}{32} {d}^4$	d = diameter of gongol