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Leonardo da Vinci’s Polyhedra and Intarsia


Art, Math  


5, 6, 7, 8  

Title – Leonardo da Vinci’s Polyhedra and Intarsia

By – Mary Mills

Primary Subject – Art

Secondary Subjects – Math

Duration – 1 week

Note: For another multidisciplinary lesson, SEE ALSO Did Leonardo da Vinci’s Curiosity and Detailed Drawings Influence Communities Around the World?

Subject: Da Vinci’s Illustrations for Luca Pacioli’s Geometry Book, The Divine Proportion

Subject Specific TEKS:

Perception, creative expression/performance

  • 117.11 (a1 & a2)
  • 117.11 (b 3.1a & b)
  • 117.11 (b 3.2a & c)

Technology Specific TEK:

Multiple Intelligences Addressed:

  • Bodily-kinesthetic
  • Spatial
  • Personalized learning

Main Objective/Goal:

  • TSW discover how math relates to art by designing 2-dimensional and 3-dimensional shapes and forms, observing angles and counting faces of their favorite polyhedra (polygons).

Specific Objectives:

TSW construct marshmallow-and-toothpick polyhedra of their choice from three open-faced polyhedra (polygons): octahedron, icosahedron, or rhombi-cuboctahedron. (3-dimensions)

TSW design an inlay or intarsia mosaic using marshmallows and toothpicks glued to a poster board, painting the “marshmallows” and leaving the poster or construction paper background a solid color – to create a mosaic effect. Original design will be fitted together without gaps or openings. (2-dimensions)

TSW add five new terms to their Vocabulary Notebooks and draw examples, writing a simple sentence for each term using their newly-created projects.


  • 5 pieces poster-size construction paper or poster board cut into 20 equal sections if 20 students (for mosaic)
  • 2 pieces poster paper to display finished polygons (student names added when polygon completed)
  • 4 packages miniature marshmallows (10.5 oz.)
  • Box of 1500 rounded toothpicks (wooden or plastic)
  • Paper towels 5 rolls
  • 20 paintbrushes & 20 basic watercolor sets
  • 20 capped containers to hold water to clean brushes between colors
  • Elmer’s glue (5 containers) for 2-dimension mosaics
  • 20 plastic bags for hand-made projects (to be taken home)

Focus/Anticipatory Set:

Leonardo da Vinci drew illustrations for Luca Pacioli’s math book, The Divine Proportion, using polygons (many-sided closed figures) with open faces instead of solid faces. Can you observe the pictures on pages 33 and 34 of Amazing Leonardo da Vinci Inventions You Can Build Yourself
and predict why this new way of looking at geometric angles was so revolutionary to our present understanding of how things work?

Instructional Input:

Teacher writes five new words on board, asking students to watch, then add them to their vocabulary notebooks:

  • Polygon (Polyhedra)
  • Mosaic
  • Inlay
  • Intarsia
  • Triangle

Teacher reads 2-paged article, Leonardo and Luca Pacioli’s “Divine Proportion” to class.

Teacher shows students Chapter 3 in “ A Short Walk Around the Pyramids”… identifying illustration #24 on page 31.

Teacher asks students to examine how math and geometry relate to art by adding a triangle shape to the board and showing p. 34 or 35 finished polygon shapes created by triangular patterns (Patterning).


Teacher picture-talks Amazing Leonardo da Vinci Inventions book elements:
cover, title page, contents page, introduction, flipping book to back glossary, bibliography/resources, and index.

Students observe as teacher reads Divine Proportion pages 32 & 33 to class, modeling left-to-right and top-to-bottom word flow.

Teacher shows students where subject books and dictionary are located in classroom.

Teacher compares the Internet papers on da Vinci’s icosahedron polygon to the shape of the marshmallow icosahedron on page 35, placing the polygon names on the board and noting how many sides each figure has:

  • Polyhedra (3-dimensional polygons)
  • Polygons (many-sided figures)
  • Octahedron (8-faced figure)
  • Icosahedron (20-faced figure)
  • a rhombiculoctahedron (26-faced figure).


Mosaic – Inlaid surface decoration that creates a pattern.

Intarsia – Mosaic that can include a solid OR patterned background.

Inlay – Mosaic that must have solid background.

Polyhedra or Polygons – many-sided figures that are closed.

Triangle – 3 angles.

Check for Understanding:

Teacher asks general questions throughout lesson to see if students understand math angles in art objects, the shapes and forms of objects, and the importance of proportion of objects in relation to keeping them stable.

Teacher reinforces that mosaics include inlay and intarsia patterns. Inlays have solid backgrounds and intarsia can have solid (or patterned) backgrounds.

Teacher explains again that “poly” means many and “polygons or polyhedra” are closed figures that have many sides.

Guided Practice:

Teacher makes an octahedron and a mosaic inlay example in front of the class.

Re-teaching Opportunities:

  • Students could sketch three polygons that are totally original with the only restriction being that all the sides are closed (no spaces); or,
  • A Short Walk Around the Pyramids book – Chapter 3, pages 28-33 [Look at p. 31, Illus. #24, and think about how you could design a different mosaic (inlaid surface decoration that creates a pattern)].


  • Amazing Leonardo da Vinci’s Inventions You Can Build Yourself by Maxine Anderson
  • Leonardo da Vinci for Kids: His Life and Ideas by Janis Herbert
  • A Short Walk Around the Pyramids and Through the World of Art by Philip M. Isaacson
  • Easy to Make Inlay Wood Projects – Intarsia: A Complete Pattern and Instruction Manual by Judy Gale Roberts and Jerry Booher
  • Intarsia Woodworking Projects: 21 Original Designs with Full-Size Plans and Expert Instruction for All Skill Levels By Kathy Wise
  • Fantasy and Medieval Mosaics for the Scroll Saw: 33 Patterns for Castles, Dragons, Knights, Unicorns and More by Frank Droege
  • General dictionary

Possible Connection to Other Subjects:

  • Science – Covalent bonds in chemistry (Show picture and compare p. 34-35 polyhedra (polygons) in Amazing Leonardo book to covalent bond picture from the Internet).
  • Music & Rhythm – Teacher could clap and sing terms (with students repeating) polyhedra, polygons, octahedron, icosahedron, rhombiculoctahedron, and triangle with students, followed by students counting syllables and clapping after teacher claps and sings each term.

Independent Practice:

TSW construct one polyhedra from 3 choices.

TSW design inlay using marshmallows and glue and paper.

TSW compare and contrast the Icosahedron in the Amazing Leonardo book with the teacher-supplied web pages containing two versions of the closed and open polyhedra.


Teacher asks volunteer students to consider how math relates to the art they created. Leonardo da Vinci developed new ways of looking at the world. What other inventions or ideas did he sketch that illustrate his genius? Did all of Leonardo’s creative ideas work? How have we shown our respect for da Vinci, who never stopped producing new ideas?


Teacher reads 2-page article, observing individual student responses to general questions (how math relates to art).

Teacher asks students to add 5 new terms to their Vocabulary Notebooks, reading teacher-supplied definitions of intarsia, inlay, mosaic, polygons (polyhedra), and triangle (below), drawing an original picture to remember each word and writing a sentence that relates to their own projects using the new words.

Teacher observes students constructing polygons, quietly asking each student where an angle is located and how many faces will be in their polygons when they finish them.

Student volunteers will show their inlay (intarsia) to the class, sharing their mosaic.

Teacher tests students on five main vocabulary words and completed projects (asking students to note how many sides are in their 3-dimensional polygon).


All students will take projects home to share with parents, asking them to write a note to teacher, telling her what they learned about da Vinci. No student project will be graded and all students will be praised for positive efforts put into the project. Students who do not understand polygons will be given further, simple math assignments on polygon shapes to take home (with note asking parents to help them understand shapes). Parents will receive sheet of definitions (above).


Teacher will work with resource person to adapt models to two-dimensional picture to color or describe. ESLs and other students during “Independent Time” may wish to work online in a math site to learn more about polygons.

Safety Rules:

  • Please do not eat any of these marshmallows…
  • Germs can make you very sick.
  • This hands-on project is NOT EDIBLE!

E-Mail Mary Mills!

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