Poem and parody -- isomorphic?

In mathematics, algebraic systems that have different objects but the same structure are described as isomorphic.  The parody in poetry illustrates the same idea -- a new poem is created that matches the form of a chosen poem, but uses different words.  For example, here are the opening stanzas of a poem published in 1799 by Robert Southey (1777-1843) that was later parodied by Lewis Carroll (1832-1898) in Alice's Adventures in Wonderland.

The Old Man's Comforts and How He Gained Them     by Robert Southey 

    "You are old, father William," the young man cried,
    "The few locks which are left you are grey;
    You are hale, father William, a hearty old man;
    Now tell me the reason, I pray."

    "In the days of my youth," father William replied,
    "I remember'd that youth would fly fast,
    And abus'd not my health and my vigour at first,
    That I never might need them at last."

The complete Southey poem is available at this WikiSource link.   Here is Lewis Carroll's parody of these stanzas, as recited by Alice.

    "You are old, Father William," the young man said,
    "And your hair has become very white;
    And yet you incessantly stand on your head—
    Do you think, at your age, it is right?"

    "In my youth," Father William replied to his son,
    "I feared it might injure the brain;
    But now that I'm perfectly sure I have none,
    Why, I do it again and again."

 Here's a Wikipedia link to Carroll's complete poem.

Strictly speaking, these parodied stanzas differ from isomorphisms -- which must match in a one-to-one manner (requiring a syllable-for-syllable or word-for-word match).  Still, the poet-reader may gather a feel for the idea of isomorphic as "having the same structure."

Here is another parody, this one a bit mathematical.  It is by Louis Untermeyer (1885-1977), American poet (and parodist), critic, and anthologist; Untermeyer parodies a familiar poem by Edwin Markham (1852-1940), "Outwitted" (posted on 9 December 2010).

Einstein: A Parody in the Manner of Edw-n Markh-m    by Louis Untermeyer

We drew our circle that shut him out,

This man of science who dared our doubt.

But ah, with a fourth-dimensional grin

He squared a circle that took us in.

I found Untermeyer's parody in The Mathematical Magpie, assembled by Clifton Fadiman (Simon and Schuster, 1962).