Whether the second diagram shows that regular pentagons and hexagons can not be interlocked in the given pattern to tile a floor.
Answer to Problem 20WE
Regular pentagons cannot be used to tile a floor with any other
Explanation of Solution
Given information:
This cover of a soccer ball consists of interlocking regular pentagons and regular hexagons, as shown at the figure,
Calculation:
Refer to the figure given in the text book.
The second diagram shows that the regular pentagons and hexagons cannot be interlocked in the pattern they have done in soccer ball to tile a floor.
As to form tessellate, the measure of interior
For regular pentagons measure of each interior angle is 108 degrees which is not a factor of 360 degrees, hence regular pentagons cannot be used to tile a floor with any other polygon.
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McDougal Littell Jurgensen Geometry: Student Edition Geometry
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- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning