I searched a bit on the net and found a parametrization for cross-sections of the quintic 6D Calabi-Yau, so here's the Asympote implementation:
\documentclass{standalone}
\usepackage{asymptote}
\begin{document}
\begin{asy}[width=10cm,height=10cm]
import graph3;
size3(200);
currentprojection=orthographic(3,3,2);
currentlight=light(8,10,2);
int k1, k2, n = 5;
real alpha = 0.3*pi;
// cross section of the quintic 6D Calabi-Yau manifold
triple cy(pair z) {
pair z1, z2;
if(z==(0,0)) {
z1 = exp(2*pi*I*k1/n);
z2 = 0;
} else {
z1 = exp(2*pi*I*k1/n)*exp(log(cos(I*z))*2/n);
z2 = exp(2*pi*I*k2/n)*exp(log(-I*sin(I*z))*2/n);
}
return (z2.x, cos(alpha)*z1.y + sin(alpha)*z2.y, z1.x);
}
for(k1=0; k1<n; ++k1) {
for(k2=0; k2<n; ++k2) {
surface s = surface(cy,(-1,0),(1,0.5*pi),20,20);
draw(s,yellow+orange);
}
}
\end{asy}
\end{document}
Don't know which one is shown in your "logo", but that's at least a Calabi-Yau manifold. If you view the resulting PDF with acroread, you can rotate the beast.