  New diffraction-limited speckle images of the Red Rectangle in the wavelength
range 2.1--3.3 microns with angular resolutions of 44--68 mas and previous
speckle images at 0.7--2.2 microns revealed well-resolved bright bipolar
outflow lobes and long X-shaped spikes originating deep inside the outflow
cavities. This set of high-resolution images stimulated us to reanalyze all
infrared observations of the Red Rectangle using our two-dimensional radiative
transfer code. The new detailed modeling, together with estimates of the
interstellar extinction in the direction of the Red Rectangle enabled us to
more accurately determine one of the key parameters, the distance D=710 pc with
model uncertainties of 70 pc, which is twice as far as the commonly used
estimate of 330 pc. The central binary is surrounded by a compact, massive
(M=1.2 Msun), very dense dusty torus with hydrogen densities reaching
n_H=2.5x10^12 cm^-3 (dust-to-gas mass ratio rho_d/rho~0.01). The bright
component of the spectroscopic binary HD 44179 is a post-AGB star with mass
M*=0.57 Msun, luminosity L*=6000 Lsun, and effective temperature T*=7750 K.
Based on the orbital elements of the binary, we identify its invisible
component with a helium white dwarf with Mwd~0.35 Msun, Lwd~100 Lsun, and
Twd~6x10^4 K. The hot white dwarf ionizes the low-density bipolar outflow
cavities inside the dense torus, producing a small HII region observed at radio
wavelengths. We propose an evolutionary scenario for the formation of the Red
Rectangle nebula, in which the binary initially had 2.3 and 1.9 Msun components
at a separation of 130 Rsun. The nebula was formed in the ejection of a common
envelope after Roche lobe overflow by the present post-AGB star.
