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This package is an "old-style spkg" package.

This means it cannot be installed using sage -i like "new-style spkg" packages.

The workaround is to install it with sage -p.

Quit Sage and in a terminal, run

$ sage -p polytopes_db_4d

This involves downloading the package which contains a huge (~8 GB) database, so it might take a while.

Once this is done, restart Sage and you can follow the SageMath documentation on using the palp_database of reflexive Hodge 4-polytopes:

sage: version()
'SageMath version 8.4, Release Date: 2018-10-17'

sage: from sage.geometry.polyhedron.palp_database import Reflexive4dHodge
sage: ref = Reflexive4dHodge(1, 101)
sage: next(iter(ref)).Vrepresentation()
(A vertex at (-1, -1, -1, -1),
 A vertex at (0, 0, 0, 1),
 A vertex at (0, 0, 1, 0),
 A vertex at (0, 1, 0, 0),
 A vertex at (1, 0, 0, 0))

This package is an "old-style spkg" package.

This means it cannot be installed using sage -i like "new-style spkg" packages.

The workaround is to install it with sage -p.

Quit Sage and in a terminal, run

$ sage -p polytopes_db_4d

This involves downloading the package which contains a huge (~8 GB) database, so it might take a while.

Once this is done, restart Sage and you can follow the SageMath documentation on using the palp_database of reflexive Hodge 4-polytopes:

sage: version()
'SageMath version 8.4, Release Date: 2018-10-17'

sage: from sage.geometry.polyhedron.palp_database import Reflexive4dHodge
sage: ref = Reflexive4dHodge(1, 101)
sage: next(iter(ref)).Vrepresentation()
(A vertex at (-1, -1, -1, -1),
 A vertex at (0, 0, 0, 1),
 A vertex at (0, 0, 1, 0),
 A vertex at (0, 1, 0, 0),
 A vertex at (1, 0, 0, 0))