If you want to make a flower with three-petals or a calyx with three sepals, you need a paper with equilateral triangle shape instead of square.

Regular pentagon paper would be very useful for producing a model such as five-pointed star and five-petals flower.

Regular hexagon paper would be very useful for producing a model such as six-pointed star and six-petals flower.

If you want to make a eight-pointed star or a flower with eight-petals, you need a paper with regular octagon shape instead of square. This page shows how to make an origami regular octagon from a square paper.

If you want to make a flower with sixteen-petals, you need a paper with regular hexadecagon shape instead of square. This page shows how to make an origami regular hexadecagon from a square paper.