Asphericity

Asphericity is defined as (Eq.5):

$\langle A\rangle ={\frac {\langle \mathrm {Tr} ^{2}-3M\rangle }{\langle \mathrm {Tr} ^{2}\rangle }}$

where $\mathrm {Tr}$ is the trace of the moment of inertia tensor, given by (Eq. 3)

$\mathrm {Tr} =R_{1}^{2}+R_{2}^{2}+R_{3}^{2}$

and $M$ is the sum of the three minors, given by

$M=R_{1}^{2}R_{2}^{2}+R_{1}^{2}R_{3}^{2}+R_{2}^{2}R_{3}^{2}$

where $R_{1}^{2}$, $R_{2}^{2}$ and $R_{3}^{2}$ are the three eigenvalues of the tensor. $\langle A\rangle$ ranges from 0 for a spherical structure (or any of the platonic solid structures), to 1.

See also

• Radius of gyration
• Random walk