R help - Dec 2000 - AIC in glm()

Hello,

I just trying to play around with very simple generalized models and have 
tried the following model :
 
glm(count~t1*t2,family=poisson())

on data from Jim Lindsey's book :

change
  count t1 t2
1    45  1  1
2    13  1  2
3    12  2  1
4    54  2  2       

I get :

Call:  glm(formula = change$count ~ change$t1 * change$t2, family = poisson())

Coefficients:
          (Intercept)             change$t12             change$t22
                3.807                 -1.322                 -1.242
change$t12.change$t22
                2.746

Degrees of Freedom: 3 Total (i.e. Null);  0 Residual
Null Deviance:      48.11
Residual Deviance: 6.596e-16    AIC: 28.23

My question is :

how the AIC value is computed here? Because the deviance is null, I expected 
an AIC of 2p = 8. But I'm probably missing something.

Thanks for your help,

Yvonnick Noel, PhD
U. of Lille 3
France
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