  We revisit an orbifold matrix model obtained as a restriction of the type IIB
matrix model on a Z_3-invariant sector. An investigation of its moduli space of
vacua is performed and issues related to chiral gauge theory and gravity are
discussed. Modifications of the orbifolded model triggered by Chern-Simons or
mass deformations are also analyzed. Certain vacua of the modified models
exhibit higher-dimensional behaviour with internal geometries related to fuzzy
spheres.
