Pentacontagon facts for kids
Quick facts for kids Regular pentacontagon |
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A regular pentacontagon
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| Type | Regular polygon |
| Edges and vertices | 50 |
| Schläfli symbol | {50}, t{25} |
| Coxeter diagram |      |
| Symmetry group | Dihedral (D50), order 2×50 |
| Internal angle (degrees) | 172.8° |
| Dual polygon | Self |
| Properties | Convex, cyclic, equilateral, isogonal, isotoxal |
In geometry, a pentacontagon is a special shape with fifty (50) straight sides. It's also called a pentecontagon or simply a 50-gon. Imagine a shape with 50 edges and 50 corners! The total of all the angles inside any pentacontagon adds up to 8640 degrees.
Contents
Regular Pentacontagon
A regular pentacontagon is a very balanced shape. This means all its 50 sides are exactly the same length, and all its 50 angles are exactly the same size.
Angles and Measurements
For a regular pentacontagon, each inside angle measures 172 and 4/5 degrees (172.8°). This is a very wide angle, almost a straight line! Because of this, each outside angle (the angle you'd turn if you walked around the shape) is quite small, only 7 and 1/5 degrees (7.2°).
How It's Made
It's interesting to know that you cannot draw a perfect regular pentacontagon using only a compass and a straightedge. These are the basic tools used in classic geometry for drawing shapes. This is because the number 50 (which is 2 multiplied by 5 squared) doesn't fit the special rules for shapes that can be drawn this way.
Dissecting a Pentacontagon
Did you know you can cut a regular pentacontagon into many smaller shapes? A mathematician named Coxeter discovered that any polygon with an even number of sides (like our 50-sided pentacontagon) can be cut into smaller diamond-like shapes called rhombs.
For a regular pentacontagon, which has 50 sides, it can be divided into 300 rhombs! These rhombs are arranged in 12 groups, with 25 rhombs in each group. This way of cutting up the shape helps us understand its structure better.
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Images for kids
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The symmetries of a regular pentacontagon. Light blue lines show subgroups of index 2. The 3 boxed subgraphs are positionally related by index 5 subgroups.
See also
In Spanish: Pentacontágono para niños
