Faceting

High school (ages 12+)
Mathematics & Numbers

Name:

Date:

Step 1 · Read the article

Open the article and read it at the level above. Then answer the questions below in your own words.

https://smallwhale.org/articles/faceting

Write what each word means, using the article.

Do not copy the article. Write two things you learned, the way you would explain them to a friend.

Answers below are taken from the article’s stored facts, so they match what the student read.

1. What is the vertex preservation?The number of vertices in a faceted object remains constant
2. What is the dual relationship?Faceting is the dual operation to stellation
3. What is faceting in geometry?Faceting is a way to change a shape by cutting parts off without adding new corners. The cuts use planes that only touch the shape where it already has corners, so no new vertices appear.
4. How does faceting keep the same corners?The planes that cut the shape only meet along the existing edges or inside the shape, so every new edge or face is made from the old corners. No new points are created.

Polytope: A geometric object with flat sides, existing in any number of dimensions.
Stellation: A geometric process of extending faces of a polyhedron to create a star-like shape.
Combinatorics: The branch of mathematics dealing with combinations of objects and their arrangements.