Q: how come there is no such thing as a cocave triangle, but as soon as you get to quadrilaterals, you can get them concave ?
A: you have to go around the cave. you can't go 'around' anything with a straight line. to make the cave you need 2 lines. so if you have 2 lines for the cave, you still need at least 2 more, to go around it. so you'd need at least 4 in total to make this work