  We report the synthesis via an indium flux method of a novel
single-crystalline compound Rh3In3.4Ge3.6 that belongs to the cubic Ir3Ge7
structure type. In Rh3In3.4Ge3.6, the In and Ge atoms choose to preferentially
occupy, respectively, the 12d and 16f sites of the Im-3m space group, thus
creating a colored version of the Ir3Ge7 structure. Like the other compounds of
the Ir3Ge7 family, Rh3In3.4Ge3.6 shows potential as a thermoelectric displaying
a relatively large power factor, PF ~ 2 mW/cmK2, at a temperature T ~ 225 K
albeit showing a modest figure of merit, ZT = 8 x 10-4, due to the lack of a
finite band gap. These figures might improve through a use of chemical
substitution strategies to achieve band gap opening. Remarkably, electronic
band structure calculations reveal that this compound displays a complex
Dirac-like electronic structure relatively close to the Fermi level. The
electronic structure is composed of several Dirac type-I and type-II nodes, and
even Dirac type-III nodes that result from the touching between a flat band and
a linearly dispersing band. This rich Dirac-like electronic dispersion offers
the possibility to observe Dirac type-III nodes and study their role in the
physical properties of Rh3In3.4Ge3.6 and related Ir3Ge7-type materials.
