File:Conical model of Fano plane.png

English: A conical model of the Fano plane which is isomorphic to the standard model (equilateral triangle with inscribed circle and three medians). The circle in red (seen in 3D perspective) corresponds to the circle in the standard model. The three ellipses in blue correspond to the outer lines, i.e., the lines which form the equilateral triangle of the standard model. The green lines correspond to the three medians of the standard model. The apex corresponds to the central point of the standard model.

Alternatively, the upper two green lines and the red circle could be compared to the sides of the equilateral triangle; the two upper, smaller blue ellipses and the middle, closer green line could be compared to the medians; and the larger blue ellipse could be compared to the circle inscribed in the equilateral triangle. (That would make an alternative isomorphism.)