The context of the thread of 'what you want to design' as following.
I like Do-It-Yourself Puppetry classes the most. All the classmates of EGRC were assigned to make a cute puppet figure by using the materials they were provided with. First, we used a Styrofoam ball to make the puppet head by pulling the sock over it. Next, we cut a piece of the non-woven cloth in the shape of its frame based on which you can design. Then, I designed a cute green crocodile with yellow dorsal fin and white teeth as a decorationon the costume. Finally, everybody presented his own work and put them together on a desk,andwe took a picture with all the special puppets. I had fun at this DIY puppetry class.
I rewrite the sentence as following. Is it acceptable?
Next, we cut a piece of the Polyester cloth to shape its frame based on which you can design.
1. Just as Gil mentioned for the socks, the cloth has not been introduced, so saying "the polyester cloth" is not really clear for the reader.
2. Contrary to what many people might tell you, it is perfectly acceptable (and in this case I argue that it is preferable) to end a sentence with a preposition. I'm not sure what Fowler's Modern English Usage says on that subject (or Garner's Modern American Usage, for that matter), but the Chicago Manual of Style agrees with this perspective.
3. To me, a frame would be something more solid than cloth and is used as a foundation to build upon (perhaps sticks of wood). If the cloth is indeed functioning in this way or if "frame" is otherwise the correct or common word in puppetry design, perhaps there is no problem there.
4. Your previous sentence uses "we" and the beginning of the sentence in question uses "we," so switching to "you" later in the sentence is a bit awkward and potentially confusing.
In any case, I wonder if the following option might work:
"Next, we each cut a piece of polyester cloth and shaped it into a frame to base the rest of the design on."
I rewrite the paragraph as following. Is it acceptaable?
First, we used a styrofoam ball to make the puppet head by pulling a sock over it. Next, we each cut a piece of polyester cloth to shape its frame based on its design. Then, I designed a cute green crocodile with a yellow dorsal fin and white teeth as a decoration on its costume.
I would probably say "based on a design" or "based on a model," but it's hard to say without more context.
In my opinion, the third sentence introduces a rather abrupt switch from "we" to "I," so personally I'd probably add a sentence (perhaps "Then, we each customized/customised our design to our liking. I designed a cute . . . ").
I would also say "decoration for its costume" (note that I am from the US and sometimes prepositions change by region, although it seems to me that "for" would work here regardless. Please correct me if I'm wrong!) :)