technifyed

Pure Mathematics + Fine Arts

Explore tessellations and design your own

Find which regular polygons tile the plane and create an Escher-style tile.

  • DifficultyBeginner
  • Estimated time1 day
  • BudgetUnder ₹250
  • ClassClass 6–9
  • TeamSolo or up to 2
  • You needHousehold materials

Prerequisites: None beyond your class work

Original · by TechnifyedArt ProjectInvestigationBeginner friendlyLow costResearch orientedTwo subjects

My projects

Overview

Find which regular polygons tile the plane and create an Escher-style tile.

Skills you will use

Angle reasoningCreative design

Safety

  • This project uses a blade or sharp tool. Cut away from your body on a cutting mat, and ask an adult to help younger students.

Materials and tools

  • Card, scissors, tape
  • Coloured pencils
  • Paper
Expected costUnder ₹250About ₹50 at most, less if you borrow parts
Estimated duration1 day5 build steps, plus the report

Step-by-step roadmap

  1. Start

    You will finish with: a table of tilings with angle sums and an original tessellation artwork.

  2. 1

    Prerequisites

    Nothing special to know first. Then collect the 3 items in the materials list.

  3. 2

    Learn

    Read up on geometry: Escher, symmetry, tessellation. Your textbook chapter and one short video are enough.

  4. 3

    Plan

    Write the brief in three lines: subject, audience and the feeling you want. Collect references and make a shot list, storyboard or sketch set.

  5. 4

    Build

    1. Test which regular polygons tile with no gaps.
    2. Explain the result using interior angles.
    3. Find the eight semi-regular tilings.
    4. Make a tile by cutting a shape from one side of a square and taping it to the other.
    5. Trace it to fill a page and colour it.
  6. 5

    Test

    Show a draft to three people from your audience and note where they lose interest or get confused.

  7. 6

    Document

    Keep the sketches, drafts and rejected versions; they show your process. Report structure

  8. 7

    Present

    Show the finished work first, then the process and the choices you made. Presentation structure

  9. 8

    Publish

    Put it online as a portfolio piece with a short write-up of the brief and process.

Expected outcome

A table of tilings with angle sums and an original tessellation artwork.

Other versions of this project

Advanced version

Classify your design's symmetry group.

Ways to do this project

Text marked "You write this" is a prompt for your own work; everything else is specific to this project.

Problem
You write thisWrite your question as: How does [what you change] affect [what you measure]?
Hypothesis
You write thisWrite it as: If [I change this], then [this will happen], because [reason].
Variables
You write thisName the one thing you change (independent), the thing you measure (dependent) and what you keep the same (controlled).

Observation table

You write thisDraw a table with one column for what you change, one for each repeat reading and one for the average.

Graph
You write thisPlot what you changed along the bottom and what you measured up the side; use a bar chart for categories and a line graph for numbers.
Results
You write thisState what the graph shows in one or two sentences, with numbers.
Conclusion
You write thisSay whether the result supports your hypothesis and why you think so.

Display board

  • Title and your name
  • Question
  • Hypothesis
  • Materials
  • Procedure (with photos)
  • Data table and graph
  • Conclusion
  • What you would do next

Questions judges ask

  • What would you change if you did this again?
  • What was your biggest source of error, and how did you reduce it?
  • Where is this idea used in real life?

Working as a team

Solo or up to 2. Suggested roles:

Concept and researchDesign or directionProductionEditingPresentation

Report and presentation

Report structure

  1. Title and brief
  2. Research and references
  3. Concept
  4. Process: sketches, drafts, experiments
  5. Final work
  6. Tools and techniques
  7. Reflection: what worked and what did not
  8. Credits and sources

Presentation structure

  1. The brief
  2. References and mood
  3. Concept
  4. Process
  5. Final work
  6. Details
  7. Reflection

Viva questions

Prepare your own answers to these before you present.

  • What is the aim of your project, in one sentence?
  • What is the principle behind it?
  • Why did you choose these materials or tools?
  • What result did you get, and was it what you expected?
  • What went wrong and how did you fix it?
  • How could this be improved or used in real life?

Resources

Source and attribution

Original

Written by Technifyed. Free to use for your own school or college project; write the report in your own words. Added 1 Oct 2026.

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