# § 2.6. From homotopy to deck transformations for the cubic spherical manifolds.

We now describe the glue algorithm due to Everitt [11] for the cubic spherical manifold . It prescribes both the face gluings and the edge gluing according to the following schemes.

## ¶ Face gluings.

After correction of an error in [39] eq. 9,

(16) |

## ¶ Edge gluing scheme.

Directed edges in a single line are glued.

(17) |

Consider now the first homotopic glue generator . Following the gluing schemes, we get the correspondence shown in Fig. 23. By use of Fig.18, each face with its edges determines the position and orientation of a copy of the cubic prototile. When the two copies touch one another, they determine a unique relative position and orientation. The isomorphic deck generator is the rotation of the 3-sphere which yields the transformation between these two positions. On the left in Fig. 22 we represent this deck generator by the positions of the prototile and its right-hand neighbour.