The Book of Ezekiel opens with a vision by the river Chebar among the Judean exiles in Babylon: a storm out of the north, four living creatures each with four faces and four wings, wheels within wheels rimmed with eyes, a firmament stretched above them, and above that a throne bearing the likeness of a human figure surrounded by fire and brightness. The scene returns with variations in chapter 10, where the creatures are identified as cherubim. The Hebrew word merkavah, chariot, is not itself used of the vision in Ezekiel 1; it became the standard term for it in later usage.
That vision became the object of a specific discipline. Maaseh Merkavah, the work of the chariot, is treated in the Mishnah as dangerous knowledge, not to be expounded even to a single student unless he is wise and understands of his own knowledge. The surviving texts of the tradition (Hekhalot Rabbati, Hekhalot Zutarti, Maaseh Merkavah, 3 Enoch), describe an ascent, described paradoxically in the sources as a descent, through seven palaces guarded at every gate and entered by means of seals and passwords, arriving at last before the throne. Preparation involved fasting, repeated chanting and set bodily postures, and much of the material consists of hymns and long lists of angelic names.
The dating is contested. The manuscripts are late and the texts were edited over long periods. Gershom Scholem placed the tradition early, in the rabbinic period, and treated it as the first chapter of Jewish mysticism; later scholarship has argued for a wider date range and for considerably less continuity with the rabbinic academies than he assumed. What is not contested is that the tradition existed and that it is the earliest layer of Jewish mysticism that can be identified at all.
There is no geometry anywhere in it. The Hekhalot texts describe palaces, gates, angels, hymns and a throne. They do not describe polyhedra.