Tocalculate:The numbers of vertices, edges and faces if every face has five edges and every edge is shared by two faces. Every face has five vertices and every vertex is shared by three faces. The sum of the number of vertices and faces is two more than the number of edges.
The number of vertices are 20, edges are 30 and faces are12.
Given information:
It is given that every face has five edges and every edge is shared by two faces. Every face has five vertices and every vertex is shared by three faces. The sum of the number of vertices and faces is two more than the number of edges.
Calculation:
Consider the given information.
Let x , y and z are the number of edges, faces and vertices respectively.
Since every face has five edges so this can be written as
Also, every edge is shared by two faces so
Every face has five vertices and every vertex is shared by three faces, so
The sum of the number of vertices and faces is two more than the number of edges.
Substitute the respective values into the above equation.
Put
Put
The number of vertices are 20, edges are 30 and faces are 12.
Chapter 3 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
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- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education