**ENGR 009: Fabricating Tessellations and Tilings** **Fall 2026** **[Matt Zucker](http://mzucker.github.io/swarthmore) and [Josh Jordan](https://www.swarthmore.edu/makerspace/makerspace-staff)** | Lecture: | Tue/Thu 11:20 AM-12:35 PM, Singer 221 | |-----------------|--------------------------------------------| | Office/Lab Hours:
  | Matt Zucker: Tue/Wed 2:30-3:30, Singer 235
Josh Jordan: Thu 2:30-3:30, Makerspace, or drop-in | | Discussion forum: | https://edstem.org/us/courses/103745/discussion | # Overview In this project-based course, students will learn the fundamentals of mathematical symmetry as it applies to tilings of the plane, sphere, and 3D space, including kaleidoscopic construction, wallpaper groups, honeycombs, and aperiodic tilings. More generally, students will explore the properties of these repeating systems through the visual and physical design of their own tilings and tessellations, while learning techniques for understanding and creating geometric patterns at different scales. Students will engage in a formal design process grounded in critique and iteration in order to produce tangible 3D artifacts using computer-aided design tools, 3D printing, mold making, and casting. ***This course does not fulfill any requirement for the Engineering major.*** # Learning goals * Recognize symmetries of planar and three-dimensional patterns * Design repeating patterns in 2D using pencil and paper or vector graphics software (e.g. Adobe Illustrator) * Design repeating patterns in 3D using appropriate software (e.g. Rhinoceros 3D) * Understand how manufacturing and fabrication processes (e.g. 3D printing, mold making, casting) constrain and influence the design process * Understand the formal design process involving idea generation, execution, critique, incorporating feedback, and iteration. # Resources ## Textbooks **Required:** * Jackson, P. (2018) [*How to make repeat patterns: a guide for designers, architects and artists.*](https://us.laurenceking.com/products/how-to-make-repeat-patterns) Laurence King. * Conway, J. H., Burgiel, H., & Goodman-Strauss, C. (2025). [*The Magic Theorem: A Greatly-expanded, Much-abridged Edition of The Symmetries of Things.*](https://themagictheorem.com/) CRC Press. **On reserve at Cornell Library:** * Fathauer, R. (2020). [*Tessellations: mathematics, art, and recreation.*](https://www.mathartfun.com/TessellationsBook/index.html) CRC Press. * Grünbaum, B., & Shephard, G. C. (1987). [*Tilings and patterns.*](https://store.doverpublications.com/products/9780486469812) Courier Dover Publications. ## Software **Rhinoceros 3D:** * [Installation instructions @ Swarthmore (ITS)](https://kb.swarthmore.edu/wiki/Rhino) -- use version 8.0 * Tutorials (overalapping -- choose whichever works for you): * [Rhino Essentials on YouTube](https://www.youtube.com/playlist?list=PLrRVLDZI7hw5hTiBRraPLOwawzbkQ6GPZ) - complete at least through Part 3 * [From Rhino](https://www.rhino3d.com/learn/?query=kind:%20jump_start&modal=null) * [LinkedIn Learning tutorials](https://www.linkedin.com/learning/topics/rhino) (needs [Swarthmore login](https://kb.swarthmore.edu/wiki/LinkedIn_Learning)) **Adobe Illustrator:** * [Installation instructions @ Swarthmore](https://kb.swarthmore.edu/wiki/Adobe_Acrobat_%26_Creative_Cloud) * Tutorials: TBA **Symmetry drawing software:** * [KaleidoPaint (iOS)](https://apps.apple.com/us/app/kaleidopaint/id518275953) * [iOrnament (iOS)](https://apps.apple.com/us/app/iornament-draw-mandala-art/id534529876) * [iOrnament lite (web)](https://imaginary.github.io/cindyjs-apps/iornament/index.html) # Requirements **Prerequisites:** Any course involving sculpture or design of physical objects or systems, for example: ENGR 017, ENGR 006, ENGR 053, ENGR 072, THEA 004A, THEA 004B, THEA 004C, THEA 004D, ARTT 006E, ARTT 005A; or permission of the instructors. Students should be comfortable with 3D design software such as Autodesk Fusion or Rhinoceros 3D. **Time:** We expect students to spend approximately 8 hours per week on this class (4 classes × 8 hours per class + [8 hours for paid student work](https://www.swarthmore.edu/student-employment/student-employment-policies) = 40 hours). Although this figure will vary from individual to individual and week to week, you should plan to commit several hours outside of class to homework, reading, and projects each week. **Discussion forum**: We will use [this EdStem forum](https://edstem.org/us/courses/103745/discussion) throughout the semester to communicate course announcements and answer questions. Please use Ed (instead of just emailing us) for all course-related communications —- this allows students to see common problems and to engage in discussions about course material. # Assignments Homework consisting of symmetry problems and/or sketching exercises will be assigned roughly weekly. Typically, homework will be assigned on Tuesday, and be due online before the start of class the following Tuesday. There will be two open-ended multi-week design projects. Deliverables will include online progress updates, in-person desk reviews, participation in critiques, final reports, and of course the tangible designed objects themselves. Grading will follow approximately the divisions shown below: * Homeworks: 35% * Projects 1 and 2: 30% each * Initial ideation/proposal: 5% * Interim updates online: 5% * Participation in critiques and responsiveness to critique: 5% * Report: 5% * Final design: 10% * Final exhibition: 5% Homework is graded on a ✓+, ✓, ✓- scale. A grade of ✓+ indicates no notable errors, ✓ indicates a sound understanding of course material, and ✓- indicates that you should spend more time reviewing the material on the assignments and/or attending office hours sessions to shore up your understanding. In lieu of a final exam, we will be hosting an opening for an on-campus exhibition of student work. Your participation in the exhibition constiututes part your class grade. ## Collaboration and attribution * Feel free to collaborate with your classmates on homework; however, you must submit your own work. Duplicating others’ assignments verbatim is prohibited. * If you do discuss homework with your classmates, We expect you to disclose any such collaboration clearly in your submitted work. Err on the side of caution – it’s the best way to avoid awkward conversations about suspicious similarities between assignments. * Cite any external sources used, including the textbooks, internet, discussions with other professors, etc. * With respect to projects, you may trade ideas with your classmates, but all design and fabrication must be your own work. Please limit the exchange of ideas to critique, suggestions, Q&A, and sketches. * If you are unsure how to design or fabricate something, please ask the instructors or post a question on the discussion forum. Aside from the course-specific policies above, you are expected to understand and abide by the college's [policy on academic misconduct](https://www.swarthmore.edu/student-handbook/academic-policies#academic_misconduct). ## AI Policy You may not use any AI systems (e.g. ChatGPT, Claude, etc.) to produce work that is turned in for this course. Prohibited uses of AI include (but are not limited to): * Consulting for homework problems (e.g. wallpaper group classification of images) * Ideation/brainstorming for projects * Generation of images, models/meshes, or code * Critique or review of your work ## Late policy, extensions, etc. Homework will generally be assigned on Tuesday, and due at the start of class the following Tuesday. Homework assignments may be turned in up to a week late for half credit. Students get one free late homework turn-in without penalty. We will be liberal in granting extensions for homeworks *when requested in advance*. The more notice and communication we have from you about your academic needs, the more help we can provide! For projects, the course policy will generally be "turn in what you have completed by the deadline". This is standard for courses in design that feature formal critique. # Accommodations If you believe you need accommodations for a disability or a chronic medical condition, please visit the [Student Disability Services website](https://www.swarthmore.edu/office-academic-success/welcome-to-student-disability-services) for details about the accommodations process. Since accommodations require early planning and are not retroactive, contact Student Disability Services as soon as possible. You are also welcome to contact us privately to discuss your academic needs. However, all disability-related accommodations must be arranged, in advance, through Student Disability Services. ***Even outside the context of accommodations for disabilities, if there is something we can do to facilitate your learning, please do not hesitate to contact us.*** # Schedule !!! Warning Please note that topics and dates are subject to change. Check this page frequently for updates, assignments, readings, etc. September 1, 2026: Introduction * Syllabus review * What is a tessellation? * Regular tilings of the plane: squares, triangles, and hexagons * Archimedian aka semiregular tilings * Dual tilings **Resources:** * [Slides from today](https://docs.google.com/presentation/d/1sPoIV_6-YiysA782MAr3Ky15ziFJ-wJMtIX7NGht2IA/edit?usp=sharing) September 3, 2026: Intro to Project 1 * [Project 1](project1.html) brief and schedule * Strategies for designing tilings (introductory) * In-class exercises (app or pencil and paper or scissors and paper) **Resources:** * [Slides from today](https://docs.google.com/presentation/d/1g_CMNETyMLJ23AF0xsmUTZM3SNgYeUuq2RsmvBSiG8Q/edit?usp=sharing) **Assignments:** * [Homework 1](homework1.html) - design a castable and tileable 3D object (due 9/10) * Before class on Tuesday: [Install Rhino](https://kb.swarthmore.edu/wiki/Rhino) and follow [YouTube tutorials](https://www.youtube.com/playlist?list=PLrRVLDZI7hw5hTiBRraPLOwawzbkQ6GPZ) (at least through Part 3) September 8, 2026: In-class design work on Homework 1 * Intro to [wallpaper groups](https://en.wikipedia.org/wiki/Wallpaper_group) * Work on Homework 1 September 10, 2026: Tiling case studies and fundamentals * Tilings in architecture and design * Fathauer Chapter 5 * Illustrator instruction for quickly painting/coloring grids * Truchet tiles * Before Tuesday: read chapter 1 of The Magic Theorem and complete exercises September 15, 2026: Pitch day for Project 1 * Project 1 pitches * Magic theorem Chapter 1 * Kaleidoscopes * Gyrations * Homework 2: Kaleidoscopes and roses exercise September 17, 2026: Moldmaking and casting * Basics of moldmaking and casting w/ live demo * DFM for casting * Heuristics * Before Tuesday: read chapter 2 of The Magic Theorem and complete exercises September 22, 2026: Ordinary symmetries * Magic Theorem Chapter 2 * combining kaleidoscopes and gyrations * miracles and wonders * recognizing ordinary symmetries (kaleidoscopes and gyrations) * Homework 3: Ordinary symmetries exercise + casting Homework 1 September 24, 2026: Work on Project 1 * Project 1 desk crits * Before Tuesday: read chapter 3 of The Magic Theorem and complete exercises September 29, 2026: Magic Theorem chapter 3 * Magic Theorem Chapter 3 * wonders and miracles * recognizing symmetries * How to shoot your work October 1, 2026: Work on Project 1 * Project 1 desk crits * Before Tuesday: read chapter 4 of The Magic Theorem and complete exercises October 6, 2026: Magic Theorem Chapter 4 * Magic theorem Chapter 4 * spherical symmetry * TBA October 8, 2026: Project 1 Critique * Project 1 critique (October 13, 2026): Fall break (October 15, 2026): Fall break October 20, 2026: Intro to Project 2 * Project 2 brief and schedule * Truchet tiles * Fathauer Chapter 18 - decorating with knots * Homework 4 from MT - spherical symmetry exercise - due Tuesday October 22, 2026: Two-part moldmaking * 2-part moldmaking demo * Exercise October 27, 2026: Aperiodic tilings, tiling strategies * Aperiodic tilings * Strategies for designing tilings * Polyforms October 29, 2026: Moldmaking and case studies * Share 2-part mold exercise * Moldmaking technologies nad examples * Case studies * Refresh project 2 November 3, 2026: Pitch day for Project 2 * Project 2 pitches November 5, 2026: Work on Project 2 * Project 2 desk crits November 10, 2026: Parquet deformations, motif design * Parquet deformations and other transformations * In-class exercise on edge swaps and motif design November 12, 2026: Technical drawing * Technical/axonometric drawing exercise November 17, 2026: TBA November 19, 2026: Work on Project 2 * Project 2 desk crits November 24, 2026: TBA (November 26, 2026): Thanksgiving December 1, 2026: Magic Theorem Chapters 6 and 7 December 3, 2026: Work on Project 2 * Project 2 desk crits December 8, 2026: Project 2 critique * Project 2 critique