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
Overview
Find which regular polygons tile the plane and create an Escher-style tile.
Skills you will use
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
Step-by-step roadmap
Start
You will finish with: a table of tilings with angle sums and an original tessellation artwork.
- 1
Prerequisites
Nothing special to know first. Then collect the 3 items in the materials list.
- 2
Learn
Read up on geometry: Escher, symmetry, tessellation. Your textbook chapter and one short video are enough.
- 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.
- 4
Build
- Test which regular polygons tile with no gaps.
- Explain the result using interior angles.
- Find the eight semi-regular tilings.
- Make a tile by cutting a shape from one side of a square and taping it to the other.
- Trace it to fill a page and colour it.
- 5
Test
Show a draft to three people from your audience and note where they lose interest or get confused.
- 6
Document
Keep the sketches, drafts and rejected versions; they show your process. Report structure
- 7
Present
Show the finished work first, then the process and the choices you made. Presentation structure
- 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).
Materials and procedure are in Materials and the Roadmap.
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?
- Research question
- You write thisOne question you can answer with data, narrow enough to finish in the time you have.
- Hypothesis
- You write thisWhat you expect to find, and why.
- Variables
- You write thisWhat you change or compare, what you measure, and what you hold constant.
- Methodology
- You write thisDescribe the method in enough detail that someone else could repeat it: sample, tools, procedure.
- Data collection
- You write thisSay what you will record, how many times, and how you will keep the records safe.
- Analysis
- You write thisChoose the table, chart or test that answers the question; report averages with their spread.
- Limitations
- You write thisList what could have affected the result: small sample, instrument limits, things you could not control.
Literature review
Find five to eight sources (your textbook, review articles, reports) and note what each says about your question. Group them by idea, not one after another, and end with what is still not known.
References
List every source you used in one style throughout (author, year, title, where it was published, link and the date you opened it).
Use this as the outline of your README or case study.
- Problem
- You write thisThe problem in one or two sentences.
- Why it matters
- You write thisWho has this problem and what it costs them.
- What was built
- A table of tilings with angle sums and an original tessellation artwork.
- Technology
- You write thisThe languages, libraries and tools you used, and why you picked them.
- Architecture
- You write thisOne diagram: the parts and how data moves between them.
- Implementation
- You write thisThe 5 build steps in your own words, with one code or design decision you are proud of.
- Challenges
- You write thisThe hardest bug or decision, and how you got past it.
- Results
- You write thisNumbers: accuracy, speed, users, survey answers.
- Demo and code
- You write thisA link to a live demo or a short video, and to the GitHub repository.
- Lessons learned
- You write thisWhat you would do differently next time.
- Future improvements
- Classify your design's symmetry group.
Working as a team
Solo or up to 2. Suggested roles:
Report and presentation
Report structure
- Title and brief
- Research and references
- Concept
- Process: sketches, drafts, experiments
- Final work
- Tools and techniques
- Reflection: what worked and what did not
- Credits and sources
Presentation structure
- The brief
- References and mood
- Concept
- Process
- Final work
- Details
- 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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