Tetrahedral hard sphere model

The tetrahedral hard sphere model consists of four hard spheres located on the vertices of a regular tetrahedron.
Second virial coefficient
The second virial coefficient is given by ([1] Eq.5):
- Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\frac {B_{2}^{*}}{4V_{m}^{*}}}=1+{\frac {UL^{*}+VL^{*3}}{4}}}
where is the reduced elongation, is the corresponding reduced volume, Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle U=0.72477} and Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle V=4.730} .
Equation of state
The equation of state is given by ([1] Eq. 17):
- Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\frac {\beta P}{\rho }}={\frac {1+(1+UL^{*}+VL^{*3})y+(1+WL^{*}+XL^{*4})y^{2}-(1+ZL^{*3})y^{3}}{(1-y)^{3}}}}
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 U=0.72477}
, 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 V=4.730}
, 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 W=1.3926}
, 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 X=24.78}
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 Z=7.69}
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