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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

Kamlesh Kumar Dubey
Invertis University, Bareilly, Uttar Pradesh, India

Bikromadittya Mondal
B.P.Poddar Inst. of Management and Technology, Kolkata, India

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.

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