Calculating the volume of convex polyhedra using GeoGebra 3D
DOI:
https://doi.org/10.23925/2237-9657.2026.v15i1p133-149Keywords:
icosidodecahedron, classes of polyhedra, nested radicalsAbstract
This article presents the decomposition of the icosidodecahedron, an Archimedean convex polyhedron that is the dual of the rhombic triacontahedron, a Catalan polyhedron. The decomposition into regular triangular and pentagonal pyramids, performed in GeoGebra 3D, aims to establish a strategy for calculating the polyhedron's volume. In the polyhedron construction stage, which precedes the decomposition stage, we imported information, such as the coordinates of the vertices and faces, from the Visual Polyhedra Platform. In the calculation of the polyhedron's volume, we converted nested radicals into sums and differences of simple radicals. We made the decomposition available on a GeoGebra platform page accessible via an external link and illustrated the process with polyhedra of other classes. The decomposition strategy proved effective in calculating the volume, which agrees with data available in the literature.
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