GeomeTricks Series: Chapter Details

This page describes the contents of each GeomeTricks book in detail, including pictures and videos of models created in each chapter.
 

Symmetry Book 1:
Mirror and Rotational Symmetry

Aperiodic Patterns Book 1:
Rotational and Spiral Tiling

Symmetry Book 2:
Spinning Sprirals

Aperiodic Patterns Book 2:
Advanced Spiral Tiling

Periodic Patterns Book 1:
Single-Polygon Patterns

Aperiodic Patterns Book 3:
Patterns Based on Fives

Periodic Patterns Book 2:
Mosaics with Regular Polygons

Fractals Book 1:
Repeating Shapes

Periodic Patterns Book 3:
Advanced Mosaics

Fractals Book 2:
Star Fractals
Periodic Patterns Book 4:
Patterns with Irregular Polygons
3D Solids Book 1:
Basic Platonic and Archimedean Solids
3D Solids Book 2:
Golden Rectangles Solids

 

 

 

 

 

 

 

 

 

 

Geometricks Symmetry Series
Book 1: Mirror and Rotational Symmetry

Flipping and Spinning Shapes in SketchUp Make 2014
For Mac and PC

87 pages (5.5" x 8'.5" printed book)
58 pages (8.5" x 11" printable PDF)

 

 

 

 

 

Chapter 1: Mirror Symmetry

This chapter will explain how to copy objects over lines of symmetry, using the Move, Rotate, and Scale tools.





 


 

Chapter 2: Rotational Symmetry

This chapter starts off with squares, and divides them into smaller squares to make pinwheel patterns. A lot of scaling is used here.



 

Chapter 3: More Rotating Patterns

This chapter explains how you can shrink or grow a polygon, and add overlappng shapes, to make neat-looking spiral and rotated patterns.




 



 

Geometricks Symmetry Series
Book 2: Spinning Spirals

Creating and Animating Patterns with Spiral Symmetry in SketchUp Make 2014
For Mac and PC

59 pages (5.5" x 8'.5" printed book)
38 pages (8.5" x 11" printable PDF)

 

 

 

 

 

Chapter 1: Spiral Patterns

In the first chapter, you'll create increasingly smaller polygons, and paint them in spiral patterns.





 

 

Chapter 2: Animating Spirals

In this chapter, you'll learn how to use layers, groups, and scenes to animate your spirals, making them look like they're spinning.

Play the movie to the right to see what we mean --->



 

 

Geometricks Periodic Patterns
Book 1: Single-Polygon Patterns

Making Tesselations with Triangles, Quadrilaterals and Hexagons in SketchUp Make 2014
For Mac and PC

34 pages (5.5" x 8'.5" printed book)
23 pages (8.5" x 11" printable PDF)

 

 

 

 

 

Chapter 1: Triangle Patterns

In the first chapter, you'll make tesselations with regular and irregular triangles.


 


 

Chapter 2: Quadrilateral Patterns

In this chapter, you'll make tesselations with regular and irregular quadrilaterals.


 

 

Chapter 3: Hexagon Patterns

In this chapter, you'll see the one and only way you can tile regular hexagons.



 

Chapter 4: Patterns with Holes 

In this chapter, you'll see what happens when you copy polygons so that holes are left between them. 

 

 

 

Geometricks Periodic Patterns
Book 2: Mosaics with Regular Polygons

Making Semi-Regular and Demi-Regular Tesselations using SketchUp Make 2014
For Mac and PC

88 pages (5.5" x 8'.5" printed book)
55 pages (8.5" x 11" printable PDF)

 

 

 

 

 

 

Chapter 1: Making Polygons

In the first chapter, you'll create a set of polygons that have identical edge lengths .


 

 

Chapter 2: Packing a Vertex

This chapter shows the various ways you can arrange polygons to completely fill the space around a vertex.
  
 

 

 

Chapter 3: Semi-Regular Patterns 

In this chapter you'll learn how to make the eight standard patterns in which each vertex is surrounded by the same polygons.

 
 

Chapter 4: Demi-Regular Patterns

In this chapter, you'll make patterns for which there can be different arrangments at each vertex.

 

Chapter 5: Coloring Mosaics

In this chapter, you'll learn a few ways you can change the colors of your patterns: keeping the pattern intact, removing the repeating pattern, and printing a "blank" mosaic for coloring by hand.

 

 

Geometricks Periodic Patterns
Book 3: Advanced Mosaics

Making Regular Tesselations into Complicated-Looking Patterns, using Google SketchUp 7
For Mac and PC

96 pages (5.5" x 8'.5" printed book)
63 pages (8.5" x 11" printable PDF)

 

 

 

 

 

Chapter 1: Making Polygons

In the first chapter, you'll create a set of polygons that have identical edge lengths .


 

 

Chapter 2: Copying a Pattern

This chapter shows what you can get when you start with a semi- or demi-regular pattern and copy it onto itself.
  
 

 

 

Chapter 3: Joining Faces 

In this chapter you'll learn how to modify patterns by removing some edges.

 

Chapter 4: Duals

In this chapter, you'll learn how to start with one pattern and create a completely different one by drawing lines between center points.


Chapter 5: Coloring Mosaics

In this chapter, you'll learn a few ways you can change the colors of your patterns: keeping the pattern intact, removing the repeating pattern, and printing a "blank" mosaic for coloring by hand.

 

Geometricks Periodic Patterns
Book 4: Patterns with Irregular Polygons

Tesselations with Pentagons and Hexagons, using SketchUp Make 2014
For Mac and PC

93 pages (5.5" x 8'.5" printed book)
66 pages (8.5" x 11" printable PDF)

 

 

 

 

 

Chapter 1: Basic Pentagon Patterns

In the first chapter, you'll learn several ways to create irregular pentagons so that they will tesselate.


 

 

Chapter 2: Round Pentagon Patterns

This chapter shows how to arrange irregular pentagons in circular tilings. 
 

 

Chapter 3: Pentagons with Some Math 

This chapter requires a bit of number-crunching, solving for edge lengths and angles to make pentagons that tile.

Chapter 4: Hexagons

In this chapter, you'll make tesselations with irregular hexagons.

 

 

Geometricks Aperiodic Patterns
Book 1: Rotational and Spiral Tiling

Shapes that make Round and Spiral Patterns, using SketchUp Make 2014
For Mac and PC

101 pages (5.5" x 8'.5" printed book)
71 pages (8.5" x 11" printable PDF)

 

 

 

 

 

Chapter 1: Tiling Triangles

In this chapter you'll make rotational and spiral tiling patterns, using isoceles, regular, and scalene triangles.
  
 

 


 

Chapter 2: Tiling Polygons

In this chapter, you'll learn how to make irregular octagons that form funky rotational and spiral patterns. 

 

 
 

 


Chapter 3: Radial Spiral Tiles

This chapter focuses on logarithmic spirals: shapes that maintain the same proportions but get progessively larger in each ring.

 



 

 

Geometricks Aperiodic Patterns
Book 2: Advanced Spiral Tiling

Creating Hirschhorn, Bent Wedge, and Voderberg Tiles, using SketchUp Make 2014
For Mac and PC

79 pages (5.5" x 8'.5" printed book)
54 pages (8.5" x 11" printable PDF)

 

 

 

 

 

Chapter 1: Hirschhorn Tile

In the first chapter, you'll learn the math behind this famous five-sided shape, and learn a few ways to tile it.  
  
 

 

 

Chapter 2: Bent Wedge

In this chapter, you'll learn the math behind this nine-sided shape, and see how it can tile. 

 

 

Chapter 3: Voderberg Tile

The math for this nine-sided tile is a little complex, requiring some creative geometric thinking.

Once you create it, you can make fantastic rotational and spiral patterns.



 

 

Geometricks Aperiodic Patterns
Book 3: Patterns Based on Fives

Creating Kepler and Penrose Tiles, using SketchUp Make 2014
For Mac and PC

91 pages (5.5" x 8'.5" printed book)
58 pages (8.5" x 11" printable PDF)

 

 

 

 

 

 

Chapter 1: Kepler Tiles

In the first chapter, you'll learn how to make some of Kepler's famous patterns, based on regular pentagons and decagons.


 

Chapter 2: Penrose Rhombs

In this chapter you'll learn the math behind Penrose's famous "fat" and "skinny" rhombs, and see how to embelish these two tiles for an infinite variety of star-based patterns.

 


Chapter 3: Penrose Kites and Darts

In this chapter you'll learn the interesting math behind Penrose's "kite" and "dart" tiles. These tiles are embellished with arcs, and together they can create wonderful rotational tilings.


 

 

Geometricks Fractals
Book 1: Repeating Shapes

Creating Rep-Tiles and Fractals, using SketchUp Make 2014
For Mac and PC

84 pages (5.5" x 8'.5" printed book)
55 pages (8.5" x 11" printable PDF)

 

 

 

 

 

 

Chapter 1: Rep-Tiles

In the first chapter, you'll learn the math behind several types of tiles, that, when repeated, form larger versions of themselves.

Chapter 2: Fractal Tiles

In this chapter, you'll start with simple shapes, and copy them to form larger, tiling shapes that interlock like jigsaw puzzle pieces.

 

Chapter 3: Sierpinksy Triangle

In this chapter you'll learn how to take a regular triangle and repeat it in increasingly larger rep-tiles, forming an infinite star.

 

Chapter 4: Pythagorean Trees

In this chapter you'll use the relationships between angles of a right triangle to make trees with increasingly smaller branches.   


 

 

Geometricks Fractals
Book 2: Fractal Stars

Creating Stars, Mosaics, and Animation, using SketchUp Make 2014
For Mac and PC

52 pages (5.5" x 8'.5" printed book)
33 pages (8.5" x 11" printable PDF)

 

 

 

 

 

Chapter 1: Fractals from Stars

In the first chapter, you'll start with a simple triangle, and rotate-copy it to make increasingly larger fractal stars .

 

Chapter 2: Fractal Mosaics

In this chapter, you'll take the stars from Chapter 1 and make mosaic patterns with them.

 

Chapter 3: Animating Star Fractals

In this chapter, you'll start out with two very different stars, and create their fractals. After using scenes and layers to animate them, you'll see the stars start to look more and more similar.

Play the movie to the right to see the fractal animation -->

 

 

 

 

 

3D Solids
Book 1: Basic Platonic and Archimedean Solids

Cubes, Octahedrons, Tetrahedrons and More,
using SketchUp Make 2014
For Mac and PC

120 pages (5.5" x 8'.5" printed book)
78 pages (8.5" x 11" printable PDF)

 

 

 

 

 

 

 

Chapter 1: Cube

In the first chapter, you'll learn a few different ways to create a cube. You'll also learn how to change a cube to get some of the simple Archimedean solids, see how a cube can be divided into pyramids, plus get a quick look at duals.

 




Chapter 2: Octahedron

In this chapter, you'll learn several ways to create an octahedron, and use it to create some more Archimedean solids. You'll also explore the relationship between the 3D octahedron and the 2D hexagon, and build an octahedron compound.
 




Chapter 3: Tetrahedron

In this chapter you'll learn how to create tetrahedrons, and explore the relationship between tetrahedrons and octahedrons.

 

 

 

 

3D Solids
Book 2: Golden Rectangle Solids

Icosahedrons, Dodecahedrons, and Some Amazing Related Solids, U sing SketchUp Make 2014
For Mac and PC

138 pages (5.5" x 8'.5" printed book)
89 pages (8.5" x 11" printable PDF)

 

 

 

 

 

 

Chapter 1: What's a Golden Rectangle?

In the first chapter, you'll learn the math behind this famed shape. You'll also learn just how often you see this shape in nature, product design, and architecture.

Chapter 2: Icosahedron

In this chapter, you'll learn how to start with just one golden rectangle and use it to build an icosahedron - a Platonic solid with 20 triangular sides. You'll also see how to create some Archimedean solids from the icosahedron, and how to find the icosahedron's dual.

 


 

Chapter 3: Dodecahedron

In this chapter you'll learn how to create a "golden 2" rectangle, and use it to make a dodecahedron. You'll also get some ideas for ways to modify your dodecahedron into some cool-looking objects.



 

Chapter 4: Compounds and Similar Objects

In this chapter you'll take what you learned about icosahedrons and dodecahedrons, and make some interesting solid compounds. You'll also see ways to create similar objects, by copying 2D objects around other 2D objects, in 3D space.