A triangle can be tiled with triangles and a square with squares, but a pentagon can’t be tiled with pentagons. At least, not in the same way, using smaller copies of the same shape. The closest you can get is this:

Pentaflake #1

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If you further subdivide the pentagon, you create what is known as a pentaflake:

Pentaflake #2

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Pentaflake #3

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Pentaflake #4

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Pentaflake (animated)

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Pentaflake (static)

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But if you bend the rules and use irregular smaller pentagons, you can tile a pentagon like this, creating what I called a pentatile:

Pentatile stage 1

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Further subdivisions create an interesting final pattern:

Pentatile #2

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Pentatile #3

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Pentatile #4

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Pentatile #5

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Pentatile #6

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Pentatile (animated)

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Pentatile (static)

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By varying the size of the central pentagon, you can create other patterns:

Pentatile #1 (animated)

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Pentatile #2 (animated)

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Pentatile #2

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Pentatile with no central pentagon

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And here are various pentatiles in an animated gif:

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And here are some variations on the pentaflake:

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Elsewhere other-posted:

• Bent for the Rent (1976) — the title of the incendiary intervention above is of course a reference to the “first and last glitter-rock album” by England’s loudest band, Spinal In Terms Of Tap
• Phrallic Frolics — more on pentaflakes