Once you see the ---, what can you get?

Question

I'm looking for an eleven-letter word.

---

The triangle you see is an equilateral triangle.

---

Note: There are four type of red lines - horizontal, vertical, left-right diagonal and right-left diagonal. All lines of the same type are considered the same. Ignore the different length and how they look.

Hint 1

Start with the red line on the triangle. And then proceed accordingly...

Answer 1

Once you see the

NET

You seem to get an

ICOSAHEDRON (11 characters)

This gives a satisfying title that

rhymes and fills in the three blanks for letters.

If we

Overlay the net of an icosahedron over the provided image, it seems to be a match -
In fact (credit op; I did not see this at first):
Flip the triangle vertically, horizontally or diagonally (depending on which line). If you start with the horizontal red line on the original triangle you would get the triangle above it.. and then proceed flipping according to the red lines, you end up with the image of the net of an icosahedron.

Original (incorrect) reasoning:
The vertical marks indicate some vertices (specifically those which 'wrap around' and need to connect top to bottom), and the other marks show the direction of lines that mark the edges.