I downloaded the PDF of the article being referenced on that website using my institution account.
Authors thoughts:
Both in the British and American samples, physical attractiveness is significantly positively associated with general intelligence, both with and without controls for social class, body size, and health. Both in the UK and in the US, the association between physical attractiveness and general intelligence is stronger among men than among women. In the UK, physically attractive men have higher IQ by 13.6 points, whereas physically attractive women have higher IQ by 11.4 IQ points. These mean differences imply bivariate correlation coefficients of r= .351 among women and r= .414 among men. Physical attractiveness is more strongly associated with general intelligence than any other variable included in the equations. However, the relatively weak
measure of physical attractiveness in the NCDS data is likely to attenuate the true association between general intelligence and physical attractiveness.
At the same time, given that the attractiveness ratings of the NCDS respondents were given by their two elementary school teachers, who were largely aware of the students' cognitive ability from their academic work, it is also possible that there may be some halo effect, where more intelligent, better students are considered by their teachers to be physically more attractive. However, such a halo effect, if it exists, does not explain where the perception that more intelligent individuals are physically more attractive comes from. The results presented in this paper suggest that the perception is based on empirical reality (Kanazawa & Kovar, 2004).
The association between intelligence and physical attractiveness is much weaker in the US. The bivariate correlations are r= .134 among women and r= .144 among men. The associations remain significant even controlling for sex, race, social class, body size, and health. The stronger association between general intelligence and physical attractiveness may possibly be due to the fact that the NCDS data have a much stronger measure of general intelligence than the Add Health data, although the latter has a stronger measure of physical attractiveness than the former. It is not clear why the association is stronger among men than among women
both in the UK and in the US, but Miller's (2000a, 2000b, Prokosch, Yeo, & Miller, 2005) general fitness factor (f-factor) model can account for the sex difference.