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

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M= R_1^2R_2^2 + R_1^2R_3^2 + R_2^2 R_3^2}

where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R_1^2} , Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R_2^2} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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

• Random walk