The Petal-Top Container can be made from any regular polygon, with an odd or even number of sides, although the instructions here are illustrated for a hexagon.  Using a polygon with few sides will make a shallow dish; using a polygon with many sides will make a taller vase.  In this web site you will find instructions for making many different polygons.  The photo below illustrates containers made from polygons with 4, 5, 6, 7, and 8 sides (clockwise, from lower right).

There is another kind of variation.  The instructions indicate in step 1 to fold the center point of each side to the center to make a smaller polygon of valley creases.  But you can also start by folding each corner of the polygon to the center to make a smaller polygon of valley creases.  The difference is illustrated by the photo below, which shows two Petal-Top Containers, both made from octagons of the same size.  The differences will be similar for other polygons. 

The container on the left used the side-to-center folding method.  It is narrower and a bit taller, with a smaller opening.  The top (white) petals are as long as the lower (colored) petals.  The petal-folds overlap each other. 

The container on the right used the corner-to-center folding method.  It is wider and a bit shorter, with a larger opening.  The top (white) petals are longer than the lower (colored) petals.  The petal-folds snuggle next to each other. 

Here is another kind of variation.  In steps 19 to 21 of the instructions, the top of each side is given a curved shape.  You can also make the shape of the top of each side straight, by matching the edges of the triangular points below the petals. 

Sturdy Petal-Top Containers can be made from card stock.  You can buy letter-size card stock from any store that sells printer paper.  Try printing one of these texture-pictures [ brush_36, brush_42, brush_90 ] on card stock, then cutting it to make a square or other polygon.  You can use the white side as the accent color, or print on both sides.  With a digital camera, try making your own texture-pictures of tile, marble, plaster, or carpeting, etc.  If you coat the finished container with clear acrylic, you can create the illusion of glazed pottery. 

To save on printer ink, you can print the texture on only the part of the page where it is needed, plus a little extra margin so that aiming the cuts will not be critical.  You can download one of these Word documents to use as a template with the margins already set up:
One 8-inch Square       Two 5-inch Squares
After you copy-and-paste the texture photo into the template, you will need to select the photo, then drag a corner to stretch it so that will cover the entire area.