Journal for Geometry and Graphics 27 (2023), No. 1, 001--009
Copyright Heldermann Verlag 2023
Volume of an n-Dimensional Polyhedron: Revisited
Abhijit Bhattacharya
B.P.Poddar Inst. of Management and Technology, Kolkata, India
bhattaabhi14@gmail.com
Kamlesh Kumar Dubey
Invertis University, Bareilly, Uttar Pradesh, India
kkdubey4maths@gmail.com
Bikromadittya Mondal
B.P.Poddar Inst. of Management and Technology, Kolkata, India
bikmondal@gmail.com
The paper presents a computational technique to determine the volume of an n-dimensional polyhedron. Initially, the volume is computed for an n-dimensional simplex which is used later to calculate the volume of an arbitrary polytope using the method of signed simplex decomposition. A recursive algorithm is used to compute the volume in n dimensions. The proposed algorithm not only calculates the volume efficiently but also avoids complex calculations in higher dimensions.
Keywords: Cayley-Menger determinant, simplex, inradius, circumradius, face angles.
MSC: 51M04; 51M05.
[ Fulltext-pdf (389 KB)]