When it comes to learning the basic shapes in German, Eva's got you covered with a video about exactly that:

Als Erstes haben wir hier einen Kreis.

First, we have a circle here.

Caption 13, Eva zeigt uns: Formen

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However, we often talk about shapes with a bit more nuance. For example, we might talk about spots and dots, or ovals rather than circles:

Alle Möbel mit roten Punkten gehören deiner Mama und die mit grünen gehören mir.

All of the pieces of furniture with red dots belong to your mother and those with green belong to me.

Caption 21, Mama arbeitet wieder Kapitel 4: Die Trennung

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Die Trainerschüler müssen die Hühner zum Beispiel dazu bringen, im Oval um zwei Kegel zu laufen.

The training students, for example, must get [their] chickens to walk around two cones in an oval.

Captions 24-25, Tierakademie Scheuerhof: Tiertrainer im Hühner-Seminar

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When we look at three-dimensional forms, there's a whole other set of vocabulary to learn. The word for a cube is actually der Kubus, but people describing objects will often use der Würfel, which is also the word you use for dice. 

Eine Masse von eineinhalb Sonnen, gepresst in eine Kugel mit gerade mal zehn Meilen Durchmesser.

A mass of one and a half suns pressed into a sphere with only a ten-mile diameter.

Captions 20-21, Unser Universum Sternengeburt: Das Leben nach dem stellaren Tod

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Wir haben hier fünfhundert Gramm Mehl, einen ganzen Würfel Hefe.

We have here five hundred grams of flour here, a whole cube of yeast.

Captions 8-9, Bundesländer und ihre Rezepte: Bayern

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Even though most patterns are repetitions of certain shapes, most of the words don't relate to the original forms. This makes sense, because even if a stripe is technically a long, thin rectangle, we don't perceive it as such. 

Oh, das Muster und... und diese Farben! Es ist wirklich überwältigend, wirklich!

Oh, the pattern and... and these colors! It is really overwhelming, really!

Caption 41, Märchen - Sagenhaft: Des Kaisers neue Kleider

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Die Flagge hat oben und unten einen roten Streifen.

The flag has a red stripe on the top and bottom.

Caption 48, Bundesländer und ihre Rezepte: Bundesland Berlin

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Ein gestreiftes Hemd und eine warme Hose und ganz schicke Schuhe.

A striped shirt and warm trousers and very stylish shoes.

Caption 17, Nicos Weg: Schick!

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In case you are like Nico and also like wearing patterned clothing, you might like to know that the word for "polka-dotted" is gepunktet, and kariert means "plaid," "checked," or "checkered." 

Further Learning
After you watch Eva's video on Yabla German in its entirety, look up the German words for some 3-D forms such as the pyramid, cone, cylinder, and prism.