The Steiner surfaces are self-intersecting embeddings of the real projective plane into three-dimensional space. More particularly, they are linear projections of a six-dimensional embedding called the Veronese surface, which is the image of an ordinary 2-sphere centered at the origin under the map f(x, y, z) = (x2, y2, z2, yz, xz, xy). There are ten different types, including the Roman surface and cross-cap.
They are named after Jakob Steiner who discovered them.
Steiner's father was a huntsman in the service of Count Hoyos in Geras, and later became a telegraph operator and stationmaster on the Southern Austrian Railway.
Steiner argued that increased autonomy for the three spheres would not eliminate their mutual influence, but would cause that influence to be exerted in a more healthy and legitimate manner, because the increased separation would prevent any one of the three spheres from dominating.
Steiner also occasionally averred that this consciousness of the spirit was not so much related to the content of his statements, where he tells readers the characteristics of this or that spiritual being (or something similar) that he says he has perceived.
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