We begin with the case of  the 8*8*8 tiling

Zett[x_]=Sqrt[(Cosh[x]-1)/(Cosh[x]+1)]

Phee1=Pi/3
Thet1=Pi/8
C1=N[ArcCosh[Cot[Phee1]*Cot[Thet1]]]
A1=ArcSinh[Sinh[C1]*Sin[Phee1]]

Zett[A1]
Zett[C1]

Now consider the 7*7*7 tiling

Phee2=Pi/3
Thet2=Pi/7
C2=N[ArcCosh[Cot[Phee2]*Cot[Thet2]]]
A2=ArcSinh[Sinh[C2]*Sin[Phee2]]

Zett[A2]
Zett[C2]

And the 6*6*6*6 tiling

Phee3=Pi/4
Thet3=Pi/6
C3=N[ArcCosh[Cot[Phee3]*Cot[Thet3]]]
A3=ArcSinh[Sinh[C3]*Sin[Phee3]]

Zett[A3]
Zett[C3]