*
Cococubed.com


Volume of Polyhedra

Home

Astronomy Research
   Radiative Opacity
   2024 Neutrino Emission from Stars
   2023 White Dwarfs & 12C(α,γ)16O
   2023 MESA VI
   2022 Earendel, A Highly Magnified Star
   2022 Black Hole Mass Spectrum
   2021 Skye Equation of State
   2021 White Dwarf Pulsations & 22Ne
   Software Instruments
     Stellar equation of states
     EOS with ionization
     EOS for supernovae
     Chemical potentials
     Stellar atmospheres

     Voigt Function
     Jeans escape
     Polytropic stars
     Cold white dwarfs
     Adiabatic white dwarfs

     Cold neutron stars
     Stellar opacities
     Neutrino energy loss rates
     Ephemeris routines
     Fermi-Dirac functions

     Polyhedra volume
     Plane - cube intersection
     Coating an ellipsoid

     Nuclear reaction networks
     Nuclear statistical equilibrium
     Laminar deflagrations
     CJ detonations
     ZND detonations

     Fitting to conic sections
     Unusual linear algebra
     Derivatives on uneven grids
     Pentadiagonal solver
     Quadratics, Cubics, Quartics

     Supernova light curves
     Exact Riemann solutions
     1D PPM hydrodynamics
     Hydrodynamic test cases
     Galactic chemical evolution

     Universal two-body problem
     Circular and elliptical 3 body
     The pendulum
     Phyllotaxis

     MESA
     MESA-Web
     FLASH

     Zingale's software
     Brown's dStar
     GR1D code
     Iliadis' STARLIB database
     Herwig's NuGRID
     Meyer's NetNuc

AAS Journals
   2024 AAS YouTube
   2024 AAS Peer Review Workshops

2024 ASU Energy in Everyday Life
2024 MESA Classroom
Outreach and Education Materials

Other Stuff:
   Bicycle Adventures
   Illustrations
   Presentations



Contact: F.X.Timmes
my one page vitae,
full vitae,
research statement, and
teaching statement.

A pre-requisite to figuring out the volume of a cube cut by a plane is to calculate the volume of a polyhedron, be it convex or non-convex.

The tool and data in polyhedra_volume.tbz compute the volume for 10 tetrahedra, 5 cubes, 5 regular octahedra, 5 rhombic dodecaheda, 1 regular dodecahedron, 1 regular icosahedron, 1 rhombic triacontahedron, 1 disdyakis triacontahedron (left image below), 1 snub cube, and 1 small stellated dodecahedron (non-convex, right image below). Guidance is given in the tool on how to create data files for other polyhedra. The calculated volumes of these polyhedra are then compared to the volumes given by Mathematica, with the differences shown to be near floating point zero.






* *
 



Please cite the relevant references if you publish a piece of work that use these codes, pieces of these codes, or modified versions of them. Offer co-authorship as appropriate.