Dodecahedron surface area and volume (TheAlgorithms#6606)

* Hexagonal number sequence 

A hexagonal number sequence is a sequence of figurate numbers where the nth hexagonal number hₙ is the number of distinct dots in a pattern of dots consisting of the outlines of regular hexagons with sides up to n dots, when the hexagons are overlaid so that they share one vertex.

This program returns the hexagonal number sequence of n length.

* Update hexagonalnumbers.py

* Update hexagonalnumbers.py

* Update hexagonalnumbers.py

* Update hexagonalnumbers.py

* Update and rename hexagonalnumbers.py to hexagonal_numbers.py

* Length must be a positive integer

* Create dodecahedron.py

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Co-authored-by: Paul <[email protected]>

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Co-authored-by: Christian Clauss <[email protected]>
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maths/dodecahedron.py

@@ -0,0 +1,73 @@
+# 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()