A regular pentagon and a regular octagon cannot tessellate on their own correct?
No. Unless you use pentagons and octagons in a configuration similar to what is commonly found on a soccer ball
thank you, i thought so
I have no clue
Thank you I thought so
What you saying
That's correct! A regular pentagon and a regular octagon cannot tessellate on their own because the internal angles of a regular pentagon are 108 degrees, while the internal angles of a regular octagon are 135 degrees. In order for shapes to tessellate, the sum of their internal angles must evenly divide into 360 degrees, which is the total sum of the angles around a point.
To verify this, you can calculate the sum of the interior angles of each shape. In a regular pentagon, there are five internal angles, each measuring 108 degrees. So, the total sum of the interior angles of a regular pentagon is 5 * 108 = 540 degrees.
In a regular octagon, there are eight internal angles, each measuring 135 degrees. So, the total sum of the interior angles of a regular octagon is 8 * 135 = 1080 degrees.
Since neither 540 nor 1080 evenly divide into 360 degrees, the regular pentagon and the regular octagon cannot fit together perfectly without leaving gaps or overlaps when attempting to create a tessellation.