devoted to the study of temari and mathematics
In G4n there are vertices with 2 α angles and 2 β angles. At a four way intersection the angles must be equal and are then 90 degree angles. So, α = β = 90.
In the I8n tilings there are vertices with 4 β and 2 γ angles. They will only be divisions if β = γ. This only occurs for n = 3 with β = γ = 60°. That is the I24 case.