#include <iostream>
#include <cmath>

////////////////////////////////////////////////////////////////
// Volumes and surface areas of the five Platonic solides
//  - This collection of functions will return the volumes
//    and surface areas of the five Platonic solids:
//                       Faces   Shape     Vertices  Edges
//        tetrahedron      4    triangle       4       6
//        cube             6    square         8      12
//        octahedron       8    triangle       6      12
//        dodecahedron    12    pentagon      20      30
//        icosahedron     20    triangle      12      30
////////////////////////////////////////////////////////////////

// Function declarations
int main();
double tetrahedron_volume( double side );
double cube_volume( double side );
double octahedron_volume( double side );
double dodecahedron_volume( double side );
double icosahedron_volume( double side );

double tetrahedron_area( double side );
double cube_area( double side );
double octahedron_area( double side );
double dodecahedron_area( double side );
double icosahedron_area( double side );

// Function definitions

int main() {
	std::cout << "The volume of a tetrahedron with a side length "
	          << 2.0 << " is " << tetrahedron_volume( 2.0 )
		  << std::endl;
	std::cout << " - expecting 0.942809041582" << std::endl;

	std::cout << "The volume of a cube with a side length "
	          << 2.0 << " is " << cube_volume( 2.0 )
		  << std::endl;
	std::cout << " - expecting 8" << std::endl;

	std::cout << "The volume of an octahedron with a side length "
	          << 2.0 << " is " << octahedron_volume( 2.0 )
		  << std::endl;
	std::cout << " - expecting 3.77123616633" << std::endl;

	std::cout << "The volume of a dodecahedron with a side length "
	          << 2.0 << " is " << dodecahedron_volume( 2.0 )
		  << std::endl;
	std::cout << " - expecting 61.3049516850" << std::endl;

	std::cout << "The volume of an icosahedron with a side length "
	          << 2.0 << " is " << icosahedron_volume( 2.0 )
		  << std::endl;
	std::cout << " - expecting 17.4535599250" << std::endl;


	std::cout << "The surface area of a tetrahedron with a side length "
	          << 2.0 << " is " << tetrahedron_area( 2.0 )
		  << std::endl;
	std::cout << " - expecting 6.92820323028" << std::endl;

	std::cout << "The surface area of a cube with a side length "
	          << 2.0 << " is " << cube_area( 2.0 )
		  << std::endl;
	std::cout << " - expecting 24" << std::endl;

	std::cout << "The surface area of an octahedron with a side length "
	          << 2.0 << " is " << octahedron_area( 2.0 )
		  << std::endl;
	std::cout << " - expecting 13.8564064606" << std::endl;

	std::cout << "The surface area of a dodecahedron with a side length "
	          << 2.0 << " is " << dodecahedron_area( 2.0 )
		  << std::endl;
	std::cout << " - expecting 82.5829152283" << std::endl;

	std::cout << "The surface area of an icosahedron with a side length "
	          << 2.0 << " is " << icosahedron_area( 2.0 )
		  << std::endl;
	std::cout << " - expecting 34.6410161514" << std::endl;

	return 0;
}

//////////////////////////////////////////////////////////
// Volume of a tetrahedron
//
// @author    Douglas Wilhelm Harder
// @date      2018-09-17
// @version   1.0
//
// @param side the length of a side of the tetrahedron
// @return     the volume of the tetrahedron
//              - the units of the return value is the cube
//                of the units of whatever the user passed
//              - if the user passes inches,
//                      the result is cubic inches
//              - if the user passes cm,
//                      the result is cm^3
//
// @section FORMULA
//   If 's' is the length of a side:
//                3 /    _
//               s / 6 \/2
//////////////////////////////////////////////////////////

double tetrahedron_volume( double side ) {
	return side*side*side/(6.0*std::sqrt(2.0));
}

//////////////////////////////////////////////////////////
// Volume of a cube
//
// @author    Douglas Wilhelm Harder
// @date      2018-09-17
// @version   1.0
//
// @param side the length of a side of the cube
// @return     the volume of the cube
//              - the units of the return value is the cube
//                of the units of whatever the user passed
//              - if the user passes inches,
//                      the result is cubic inches
//              - if the user passes cm,
//                      the result is cm^3
//
// @section FORMULA
//   If 's' is the length of a side:
//                3
//               s
//////////////////////////////////////////////////////////

double cube_volume( double side ) {
	return 0.0;
}

//////////////////////////////////////////////////////////
// Volume of a octahedron
//
// @author    Douglas Wilhelm Harder
// @date      2018-09-17
// @version   1.0
//
// @param side the length of a side of the octahedron
// @return     the volume of the octahedron
//              - the units of the return value is the cube
//                of the units of whatever the user passed
//              - if the user passes inches,
//                      the result is cubic inches
//              - if the user passes cm,
//                      the result is cm^3
//
// @section FORMULA
//   If 's' is the length of a side:
//               1   _  3
//               - \/2 s
//               3
//////////////////////////////////////////////////////////

double octahedron_volume( double side ) {
	return 0.0;
}

//////////////////////////////////////////////////////////
// Volume of a dodecahedron
//
// @author    Douglas Wilhelm Harder
// @date      2018-09-17
// @version   1.0
//
// @param side the length of a side of the dodecahedron
// @return     the volume of the dodecahedron
//              - the units of the return value is the cube
//                of the units of whatever the user passed
//              - if the user passes inches,
//                      the result is cubic inches
//              - if the user passes cm,
//                      the result is cm^3
//
// @section FORMULA
//               1          _   3
//               - (15 + 7\/5) s
//               4
//////////////////////////////////////////////////////////

double dodecahedron_volume( double side ) {
	return 0.0;
}

//////////////////////////////////////////////////////////
// Volume of a icosahedron
//
// @author    Douglas Wilhelm Harder
// @date      2018-09-17
// @version   1.0
//
// @param side the length of a side of the icosahedron
// @return     the volume of the icosahedron
//              - the units of the return value is the cube
//                of the units of whatever the user passed
//              - if the user passes inches,
//                      the result is cubic inches
//              - if the user passes cm,
//                      the result is cm^3
//
// @section FORMULA
//               5        _   3
//              -- (3 + \/5) s
//              12
//////////////////////////////////////////////////////////

double icosahedron_volume( double side ) {
	return 0.0;
}

//////////////////////////////////////////////////////////
// Surface area of a tetrahedron
//
// @author    Douglas Wilhelm Harder
// @date      2018-09-17
// @version   1.0
//
// @param side the length of a side of the tetrahedron
// @return     the surface area of the tetrahedron
//              - the units of the return value is the cube
//                of the units of whatever the user passed
//              - if the user passes inches,
//                      the result is square inches
//              - if the user passes cm,
//                      the result is cm^2
//
// @section FORMULA
//   If 's' is the length of a side:
//                     _  2
//                   \/3 s
//////////////////////////////////////////////////////////

double tetrahedron_area( double side ) {
	return 0.0;
}

//////////////////////////////////////////////////////////
// Surface area of a cube
//
// @author    Douglas Wilhelm Harder
// @date      2018-09-17
// @version   1.0
//
// @param side the length of a side of the cube
// @return     the surface area of the cube
//              - the units of the return value is the cube
//                of the units of whatever the user passed
//              - if the user passes inches,
//                      the result is square inches
//              - if the user passes cm,
//                      the result is cm^2
//
// @section FORMULA
//   If 's' is the length of a side:
//                2
//             6 s
//////////////////////////////////////////////////////////

double cube_area( double side ) {
	return 0.0;
}

//////////////////////////////////////////////////////////
// Surface area of a octahedron
//
// @author    Douglas Wilhelm Harder
// @date      2018-09-17
// @version   1.0
//
// @param side the length of a side of the octahedron
// @return     the surface area of the octahedron
//              - the units of the return value is the cube
//                of the units of whatever the user passed
//              - if the user passes inches,
//                      the result is square inches
//              - if the user passes cm,
//                      the result is cm^2
//
// @section FORMULA
//   If 's' is the length of a side:
//                   _  2
//               2 \/3 s
//////////////////////////////////////////////////////////

double octahedron_area( double side ) {
	return 0.0;
}

//////////////////////////////////////////////////////////
// Surface area of a dodecahedron
//
// @author    Douglas Wilhelm Harder
// @date      2018-09-17
// @version   1.0
//
// @param side the length of a side of the dodecahedron
// @return     the surface area of the dodecahedron
//              - the units of the return value is the cube
//                of the units of whatever the user passed
//              - if the user passes inches,
//                      the result is square inches
//              - if the user passes cm,
//                      the result is cm^2
//
// @section FORMULA
//                    ____________
//                   /          _   2
//               3 \/ 25 + 10 \/5  s
//////////////////////////////////////////////////////////

double dodecahedron_area( double side ) {
	return 0.0;
}

//////////////////////////////////////////////////////////
// Surface area of a icosahedron
//
// @author    Douglas Wilhelm Harder
// @date      2018-09-17
// @version   1.0
//
// @param side the length of a side of the icosahedron
// @return     the surface area of the icosahedron
//              - the units of the return value is the cube
//                of the units of whatever the user passed
//              - if the user passes inches,
//                      the result is square inches
//              - if the user passes cm,
//                      the result is cm^2
//
// @section FORMULA
//                  _  2
//              5 \/3 s
//////////////////////////////////////////////////////////

double icosahedron_area( double side ) {
	return 0.0;
}