Hyperspaces that satisfy $cc$-homogeneous cone condition on canonical Heisenberg and Engel groups

We get a new proof that hyperspace $\{(x,y,t)\mid t>0\}$ of canonical Heisenberg group $\mathbb {H}^1$ satisfies inner and outer continuously deformable $cc$-homogeneous cone conditions and $cc$-uniformity condition. By means of that we prove that hyperspace $\{(x,y,t,z)\mid t>0\}$ of canonical Engel group $\mathbb {E}_{\alpha,\beta}$ satisfies inner and outer continuously deformable $cc$-homogeneous cone conditions.