Here's another suggestion: "The Captured Cross-Section" by Miles J. Breuer,
M.D., same guy who wrote "The Gostak and the Doshes". Reprinted (from a 1929
_Amazing_) in Clifton Fadiman's _Fantasia Mathematica_.
http://www.isfdb.org/cgi-bin/title.cgi?54634
Here is the opening paragraph:
[BEGIN QUOTE]
The head of Jiles Heagey, Instructor in Mathematics, was bent low over
the sheets of figures; and becomingly close to it, leaned the curly-haired
one of his fiancee, Sheila Mathers, daughter of the Head of the
Mathematics Department. Sheila was no mean mathematician herself,
and had published some original papers.
[END QUOTE]
Here is the description of the 4D being:
[BEGIN QUOTE]
There in front of them was a rapidly moving object; it bounced
up and down off the floor to a height of three feet about once a
second. It did not have the harmonic motion of a bouncing body,
however; it stopped abruptly up in the air and shot downward at high
speed, hit the floor, stopped a moment and shot back upward. Then
it stopped suddenly and hung in the air. It was about the size of a
large watermelon, and looked for all the world like human skin:
smooth, uniform, unbroken all around.
The two stared at it amazed. Heagey walked up and touched it
with the tip of a finger. It grew smaller. And suddenly it decreased
to about one-half of its former size, retaining its surface smoothness
and uniformity unchanged.
It had felt soft and warm, like human flesh.
Now it was increasing in size again, while they stared gasping,
speechless, at it. When it stopped growing suddenly, it was the size
of a big barrel, with rounded ends. There was a bulging ridge around
the middle, on each side of which was a dark brown strap of something
like leather. The rest of it was just naked skin.
Sheila and Heagey stood rooted to the spot, staring at it. and at each
other. What was the thing? Where had it come from?
The Thing began thumping up and down off the floor again, with
great, thudding shocks. After a while it desisted and lay still. It was
a most uncouth, hideous-looking thing: a great lump of naked flesh
with two straps around it. It looked exactly like some huge tumor in
a medical museum, or like some monstrosity of birth. Could it be alive?
Both of them approached it cautiously. Heagey pricked it with a pin.
The skin was tough and he jabbed hard. A drop of blood appeared.
Then there was a terrible commotion. The object decreased in size
to a small sphere like a baseball. In fact, there were several
baseball-sized lumps of flesh all around; just naked flesh. They moved
rapidly, and two of them were between him and Sheila. Two or three were
on the far side of her. He counted ten of them altogether. Five of them
closed swiftly around her. Then she was gone!
[END QUOTE]