We present the results of a spectroscopic multisite campaign for the \beta Cephei star 12 ( DD ) Lacertae .
Our study is based on more than thousand high-resolution high S/N spectra gathered with 8 different telescopes in a time span of 11 months .
In addition we make use of numerous archival spectroscopic measurements .
We confirm 10 independent frequencies recently discovered from photometry , as well as harmonics and combination frequencies .
In particular , the SPB-like g-mode with frequency 0.3428 { d } ^ { -1 } reported before is detected in our spectroscopy .
We identify the four main modes as ( \ell _ { 1 } ,m _ { 1 } ) = ( 1 , 1 ) , ( \ell _ { 2 } ,m _ { 2 } ) = ( 0 , 0 ) , ( \ell _ { 3 } ,m _ { 3 } ) = ( 1 , 0 ) and ( \ell _ { 4 } ,m _ { 4 } ) = ( 2 , 1 ) for f _ { 1 } = 5.178964 { d } ^ { -1 } , f _ { 2 } = 5.334224 { d } ^ { -1 } , f _ { 3 } = 5.066316 { d } ^ { -1 } and f _ { 4 } = 5.490133 { d } ^ { -1 } , respectively .
Our seismic modelling shows that f _ { 2 } is likely the radial first overtone and that the core overshooting parameter \alpha _ { ov } is lower than 0.4 local pressure scale heights .