Surpeton pentavolume

The surpeton pentavolume of a shape is the sum of all of that shape's peta. It can be considered to be the total extent of all of the shape's 5-subfacets in five-dimensional space. The surpeton pentavolume of a polyteron is typically just called its pentavolume.

It has dimensions of [length]⁵.

Surpeton Pentavolume Formulae

5 Dimensions

Shape	Bulk Formula	Variables
Penteract	$a_1 a_2 a_3 a_4 a_5$	a1, a2, a3, a4, a5 = edge lengths
Tessinder	$\frac{\pi}{4} a_1 a_2 a_3 d^2$	a1, a2, a3 = edge lengths, d = diameter of disc
Duocyclinder	$\frac{\pi^2}{16} a d_1^2 d_2^2$	a = edge length, d1, d2 = diameters of discs
Spherisquare	$\frac{\pi}{6} a_1 a_2 d^3$	a1, a2 = edge lengths, d = diameter of ball
Cyclosphere	$\frac{\pi^2}{24} d_1^2 d_2^3$	d1 = diameter of disc, d2 = diameter of ball
Glominder	$\frac{\pi^2}{32} a d^4$	a = edge length, d = diameter of gongol
Pentorb	$\frac{\pi^2}{60} d^5$	d = diameter of pentorb