  We introduce and systematically study an expansive class of "orbifold Higgs"
theories in which the weak scale is protected by accidental symmetries arising
from the orbifold reduction of continuous symmetries. The protection mechanism
eliminates quadratic sensitivity of the Higgs mass to higher scales at one loop
(or more) and does not involve any new states charged under the Standard Model.
The structures of the Higgs and top sectors are universal and determined
exclusively by group theoretical considerations. The twin Higgs model fits
within our framework as the simplest example of an orbifold Higgs. Our models
admit UV completions as geometric orbifolds in higher dimensions, and fit
naturally within frameworks of low scale gauge coupling unification.
