Introduction to 3D Objects – What is a 3D Object?

I have been fascinated with “geometric” needlework since I began doing counted canvaswork about 20 years ago.  Recently, I have been intrigued with the idea of finishing my needlework as 3D objects.  In my research of these objects, I found a great book and related website that really launched my explorations in this area.  “Math Lab for Kids: Fun, Hands-on Activities for Learning with Shapes, Puzzles, and Games” by Rebecca Rapoport and J. Yoder and its associated website is an amazing resource for this topic and has wonderful downloadable templates for use.  In addition to that website, there is a great website that provides detailed instructions for drawing polygons found here.  I am including photos of some of my paper mock-ups, searches for “types of 3D shapes” will give you other images.

First we are going to start our discussion with some basic definitions of typical 3D objects: prism, antiprism, pyramid, and platonic solid.

  • The following shapes are platonic solids: cube, tetrahedron, octahedron, dodecahedron, and icosahedron.  These are solid shapes where each side is the same shape and the length of each side is the same.  Examples: cube is a solid where each of the six (6) sides is a square and a dodecahedron where each of the twelve (12) sides is a pentagon.  Here is a photo of 3 different layouts for stitching a cube.  In addition, here is a great source for free templates of platonic solids you can download.

Cube Layouts.jpg

  • The next shape we are going to discuss is a prism; almost any shape can be made into a prism.  A prism is a solid shape where each side is a rectangle and the top & bottom are exactly the same but can be any shape.  Example: top and bottom are pentagons and the five sides are rectangles or top and bottom are triangles and the 3 sides are rectangles.  Here is a photo of my paper mock-ups of a pentagonal prism and a triangular prism.

Pentagonal & Triangular Prisms.jpg

  • The next shape we are going to discuss is an antiprism.  Similar to the prism, the top and bottom shapes are the same but are not directly above/below each other but twisted instead.  The other difference is that the sides are made up of triangles instead of rectangles.  Due to the difference in alignment between the top and bottom shapes, it takes 2 triangular sides for each side of the “base” shape.  For example, a hexagonal antiprism would need 12 triangular sides.  Here is a photo of my paper mock-up of a hexagonal antiprism.

Hexagonal Antiprism.jpg

  • The last shape we are going to discuss is a pyramid; almost any shape can be the base of a pyramid.  A pyramid is a solid shape where each side is a triangle with a base made from any shape where all of the sides join at a single point at the top.  Here are the photos of my paper mock-up of a octagonal pyramid.

Octagonal pyramid

Octagonal pyramid #2.jpg

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