Some theorems about polyhedra

1. If five faces of a distorted cube are cyclic quadrilaterals, then
the sixth is too.
2. If five faces of a distorted cube are quadrilaterals-of-tangents
(QOTs), then the sixth is too,
3. If all-but-one of the faces of a trihedral polyhedron are cyclic,
then the last is too.
4. If all-but-one of the faces of a polyhedron-with-quadrilateral-
faces is a QOT, then the last is too.

Does anyone recognise these theorems?
If not, you saw them here first!

Tim Robinson
.

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