| \ ____|____\ | \
| | | | | |
|_____|____| | | |
\ | \ | \ |
\ | \ | \ |
\|_________\| \ __________|

Once more we ascended into space. "Hitherto," said the Sphere, "I have
shewn you naught save Plane Figures and their interiors. Now I must
introduce you to Solids, and reveal to you the plan upon which they are
constructed. Behold this multitude of moveable square cards. See, I
put one on another, not, as you supposed, Northward of the other, but
ON the other. Now a second, now a third. See, I am building up a
Solid by a multitude of Squares parallel to one another. Now the Solid
is complete, being as high as it is long and broad, and we call it a
Cube."

"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.

But still I could not fully understand the meaning of what my Teacher
had told me concerning "light" and "shade" and "perspective"; and I did
not hesitate to put my difficulties before him.

Were I to give the Sphere's explanation of these matters, succinct and
clear though it was, it would be tedious to an inhabitant of Space, who
knows these things already. Suffice it, that by his lucid statements,
and by changing the position of objects and lights, and by allowing me
to feel