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Tessellation of an Equilateral Pentagon

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3D model description

Tessellating Equilateral Pentagon
This is a simple tessellating pattern: an equilateral pentagon, four of which make a hexagon. Of course, it is not a regular pentagon. But it has interesting properties. Within each pentagon, there are two right angles, the measure of the other three angles are to be calculated.

I first figured out the measure of one of the two congruent angles, which is 45° + arccos(sqrt(2)/4). Then, I mirrored the sketches around. This makes a nice starting design project for students.

Included are two shelled pentagons, a pentagonal caddy, and a hexagonal caddy. The edge length of a pentagon is 25 mm. It is 3.6 mm in thickness. The caddy is 60 mm tall.

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3D printer file information

  • 3D design format: STL Folder details Close
    • HexagonCaddy4.stl
    • PentagonCaddy.stl
    • PentagonCaddy1.stl
    • pentagon1.stl
    • pentagon2.stl

    Learn more about the formats

  • Publication date: 2018/07/26 at 15:30




STEAM educator, learning from and working with K-12 STEAM teachers to explore new ideas of teaching and engagement. I firmly believe ART is at the core of STEM learning or all human learning! I owe my ideas and designs to the hundreds of K-12 children and teachers and university professors I have had the pleasure of working with, in multiple disciplines-- math, science,engineering language arts, social studies, early childhood education and more! All mistakes, of course, are mine! There is no warranty or liability whatsoever implied or explicit behind the designs or ideas. They are all posted for their potential educational values.

When working with children, please strictly observe all safety and health procedures! Please refer to the NSTA safety guides:


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