Traperas, Dimitrios and Kanellopoulos, Nikolaos (2018), ‘An Interactive Art Application of a Proposed Fourth Spatial Dimension Cosmological Model’, International Conference on Digital Culture & AudioVisual Challenges, Ionian University, Corfu, 1-2 June

Occultist Johan Van Manen’s describes accurately a ‘fourth-dimensional globe’; i.e., a hypersphere:
[…] The fourth-dimensional globe can be better described. It was an ordinary three-dimensional globe, out of which on each side, beginning at its vertical circumference, bent tapering horns proceeded, which, with a circular bend, united their points above the globe from which they started. So three circles are formed, the lower one representing the initial globe, the upper one representing empty space, and the greater circle circumscribing the whole. If it be now understood that the upper circle [empty space] does not exist and the lower (small) circle is identical with the outer (large) circle, the impression [of the fourth-dimensional globe] will have been conveyed, at least to some extent […] (Van Manen, 1913: 58).
We propose that it is likely that Johan Van Manen envisioned not a hypersphere, but a projection to three-dimensional space of a hyper-solid that has some folds. It is this 3d visualization that he named (wrongly) “fourth-dimensional globe”.
It is also interesting that Ouspensky does not agree with his interpretation of Johan Van Manen’s “fourth-dimensional globe” schema and comments that there might be a:
[…] possibility of constructing a certain pseudo-fourth dimension which, in actual fact, lies entirely in three dimensions. In my opinion the figure is full of motion. The whole figure seems to me moving, as though constantly arising in the meeting point of the sharp ends, spreading out from there and being re-absorbed there (Ouspensky, 2005: 134-35).

References
Van Manen, J. and Leadbeater, C.W. (ed) (1913). Some Occult Experiences. Adyar, Manras, India: Theosophical Publishing House.
(described by Johan van Manen and annotated by C. W. Leadbeater)
Ouspensky, P.D. (2005). Τertium Οrganum: The Third Canon of Thought, a Key to the Enigmas of the World. New York: Cosimo Inc.