p

```
# dodecahedron.py
"""
A regular dodecahedron is a three-dimensional figure made up of
12 pentagon faces having the same equal size.
"""
def dodecahedron_surface_area(edge: float) -> float:
"""
Calculates the surface area of a regular dodecahedron
a = 3 * ((25 + 10 * (5** (1 / 2))) ** (1 / 2 )) * (e**2)
where:
a --> is the area of the dodecahedron
e --> is the length of the edge
reference-->"Dodecahedron" Study.com
<https://study.com/academy/lesson/dodecahedron-volume-surface-area-formulas.html>
:param edge: length of the edge of the dodecahedron
:type edge: float
:return: the surface area of the dodecahedron as a float
Tests:
>>> dodecahedron_surface_area(5)
516.1432201766901
>>> dodecahedron_surface_area(10)
2064.5728807067603
>>> dodecahedron_surface_area(-1)
Traceback (most recent call last):
...
ValueError: Length must be a positive.
"""
if edge <= 0 or not isinstance(edge, int):
raise ValueError("Length must be a positive.")
return 3 * ((25 + 10 * (5 ** (1 / 2))) ** (1 / 2)) * (edge**2)
def dodecahedron_volume(edge: float) -> float:
"""
Calculates the volume of a regular dodecahedron
v = ((15 + (7 * (5** (1 / 2)))) / 4) * (e**3)
where:
v --> is the volume of the dodecahedron
e --> is the length of the edge
reference-->"Dodecahedron" Study.com
<https://study.com/academy/lesson/dodecahedron-volume-surface-area-formulas.html>
:param edge: length of the edge of the dodecahedron
:type edge: float
:return: the volume of the dodecahedron as a float
Tests:
>>> dodecahedron_volume(5)
957.8898700780791
>>> dodecahedron_volume(10)
7663.118960624633
>>> dodecahedron_volume(-1)
Traceback (most recent call last):
...
ValueError: Length must be a positive.
"""
if edge <= 0 or not isinstance(edge, int):
raise ValueError("Length must be a positive.")
return ((15 + (7 * (5 ** (1 / 2)))) / 4) * (edge**3)
if __name__ == "__main__":
import doctest
doctest.testmod()
```