  Three dimensional topological insulator crystals consist of an insulating
bulk enclosed by metallic surfaces, and detailed theoretical predictions about
the surface state band topology and spin texture are available. While several
topological insulator materials are currently known, the existence and topology
of these metallic states have only ever been probed for one particular surface
orientation of a given material. For most topological insulators, such as
Bi$_{1-x}$Sb$_{x}$ and Bi$_2$Se$_3$, this surface is the closed-packed (111)
surface and it supports one topologically guaranteed surface state Dirac cone.
Here we experimentally realise a non closed-packed surface of a topological
insulator, Bi$_{1-x}$Sb$_{x}$(110), and probe the surface state topology by
angle-resolved photoemission. As expected, this surface also supports metallic
states but the change in surface orientation drastically modifies the band
topology, leading to three Dirac cones instead of one, in excellent agreement
with the theoretical predictions but in contrast to any other experimentally
studied TI surface. This illustrates the possibility to tailor the basic
topological properties of the surface via its crystallographic direction. Here
it introduces a valley degree of freedom not previously achieved for
topological insulator systems.
