  The aim of electrical impedance tomography is to reconstruct the admittivity
distribution inside a physical body from boundary measurements of current and
voltage. Due to the severe ill-posedness of the underlying inverse problem, the
functionality of impedance tomography relies heavily on accurate modelling of
the measurement geometry. In particular, almost all reconstruction algorithms
require the precise shape of the imaged body as an input. In this work, the
need for prior geometric information is relaxed by introducing a Newton-type
output least squares algorithm that reconstructs the admittivity distribution
and the object shape simultaneously. The method is built in the framework of
the complete electrode model and it is based on the Fr\'echet derivative of the
corresponding current-to-voltage map with respect to the object boundary shape.
The functionality of the technique is demonstrated via numerical experiments
with simulated measurement data.
