“Pardon me, my Lord,” replied I; “but to my eye the appearance is as of an Irregular Figure whose inside is laid open to the view; in other words, methinks I see no Solid, but a Plane such as we infer in Flatland; only of an Irregularity which betokens some monstrous criminal, so that the very sight of it is painful to my eyes.”

“True,” said the Sphere, “it appears to you a Plane, because you are not accustomed to light and shade and perspective; just as in Flatland a Hexagon would appear a Straight Line to one who has not the Art of Sight Recognition. But in reality it is a Solid, as you shall learn by the sense of Feeling.”

He then introduced me to the Cube, and I found that this marvellous being was indeed no Plane, but a Solid; and that he was endowed with six plane sides and eight terminal points called solid angles; and I remembered the saying of the Sphere that just such a creature as this would be formed by a Square moving, in Space, parallel to himself: and I rejoiced to think that so insignificant a creature as I could in some sense be called the progenitor of so illustrious an offspring.