Sierpinski Pentagon Coloring Pages

Print the Sierpinski pentagon, where a pentagon is replaced by five smaller ones that touch at their corners, each about 0.382 times as wide, a ratio tied to the golden ratio. The three outlines hold 5, 25 and then 125 pentagons.

One more sheet shows the first stages together, and another numbers the gaps of the first two steps for coloring. The five pages are gathered in a workbook.

Part of the Sierpinski Fractals collection, Last updated on Tue, 03 Nov 2026 00:31:22 GMT.

Free Printables

Sierpinski Pentagon, Step 1

Step 1 of the pentagon: 5 pentagons meeting at their corners. | zuzuzi.com

Sierpinski Pentagon, Step 2

Step 2 of the pentagon: 25 pentagons meeting at their corners. | zuzuzi.com

Sierpinski Pentagon, Step 3

Step 3 of the pentagon: 125 pentagons meeting at their corners. | zuzuzi.com

Sierpinski Pentagon, Steps 0 to 3

One pentagon becoming 5, 25 and 125, steps 0 to 3 together. | zuzuzi.com

Sierpinski Pentagon, Color by Step

Gaps numbered 1 and 2 by their step, with a key of two colors. | zuzuzi.com

Five Copies at Every Step

Unlike the triangle, the pentagon does not cut out one middle piece: it keeps five smaller pentagons in its corners, and the gaps between them form stars and slim triangles that are lovely to color.

The Golden Ratio Inside

Each new pentagon is about 0.382 times the width of the one it replaces, which is one divided by the square of the golden ratio. The pieces shrink fast, so the pages stop at step 3.

Colors That Show the Steps

On the color by step page, gaps from the first step carry a 1 and those of the second a 2. Two colors are enough to see the pattern repeat at a smaller size.

Frequently Asked Questions

How Many Pentagons Are at Each Step?

Five times more at each step: 5, then 25, then 125 at step 3.

What Does the Number 0.382 Mean?

It is the width of each new pentagon compared with the old one, about 1 divided by 2.618, the square of the golden ratio.

Who Is This Fractal For?

Anyone who enjoys geometric coloring; the first steps suit children, and the link with the golden ratio makes it a good discussion page in middle school.