The Crystal Palace is the utopia that the underground man attributes to the "gentlemen" he addresses: a rational future in which human desires have been calculated, acts recorded in a table, and nothing new needs to be decided. The narrator rejects it.
The image appears in Chapter VII of Part One, as the point of arrival of science, which will calculate acts in a table of logarithms; then the palace will rise. The polemic has a target outside the text: the novel What Is to Be Done?, by Chernyshevsky, of 1863, culminates in a utopian dream in the form of a Crystal Palace.
What the narrator fears in the palace is being unable to defy it. In Chapter X he says: "You believe in a crystal edifice, eternally unshakable, that is, one that you cannot even stick your tongue out at in secret, nor make a fig in your pocket." He would go into a henhouse to escape the rain, but "I will not accept the henhouse as a palace, out of gratitude." Earlier, in Chapter IX, he links the palace to suffering: there it is unthinkable, because suffering is doubt and negation.
He asks to be shown something better and promises to follow whoever does so. In a letter to his brother, Dostoevsky tells that the censors cut, at this point, the passage in which the narrator concluded on the need for faith and for Christ, and the trace of that cut appears in the shifting meaning of the palace throughout the text.