Mekhontsev Wedge

Author

Eric W. Weisstein
August 27, 2026

This notebook downloaded from https://mathworld.wolfram.com/notebooks/Polyhedra/MekhontsevWedge.nb.

For more information, see Eric's MathWorld entry https://mathworld.wolfram.com/MekhontsevWedge.html.

Copyright 2026 Wolfram Research, Inc. except for portions noted otherwise

Additional Authors

Coordinate data and rep-8 subdivision from Dmitry Mekhontsev, as documented by Ed Pegg, Jr. (2026).

Definitions

mekhontsevWedgePoints = {{0, 0, 0}, {2, 0, 0}, {2, 2, 0}, {1, 1, 1}, {2, 1, 1}, 
    {2, 2, 1}}; mekhontsevWedgePieces = {{{0, 0, 0}, {2, 0, 0}, {2, 2, 0}, {1, 1, 1}, {2, 1, 1}, 
     {2, 2, 1}}, {{1, 1, 1}, {3, 1, 1}, {3, 3, 1}, {2, 2, 2}, {3, 2, 2}, {3, 3, 2}}, 
    {{4, 4, 0}, {4, 2, 0}, {2, 2, 0}, {3, 3, 1}, {3, 2, 1}, {2, 2, 1}}, 
    {{4, 0, 0}, {2, 0, 0}, {2, 2, 0}, {3, 1, 1}, {2, 1, 1}, {2, 2, 1}}, 
    {{4, 0, 0}, {4, 2, 0}, {2, 2, 0}, {3, 1, 1}, {3, 2, 1}, {2, 2, 1}}, 
    {{4, 0, 0}, {4, 2, 0}, {4, 2, 2}, {3, 1, 1}, {3, 2, 1}, {3, 2, 2}}, 
    {{4, 4, 0}, {4, 2, 0}, {4, 2, 2}, {3, 3, 1}, {3, 2, 1}, {3, 2, 2}}, 
    {{4, 4, 0}, {4, 4, 2}, {4, 2, 2}, {3, 3, 1}, {3, 3, 2}, {3, 2, 2}}}; 
  mekhontsevWedgeFaces = {{1, 2, 3}, {4, 5, 6}, {1, 2, 5, 4}, {2, 3, 6, 5}, {1, 3, 6, 4}}; 
  MekhontsevWedge[] := Graphics3D[{Directive[ColorData[97][1], Opacity[0.75]], 
     EdgeForm[Directive[LightDarkSwitched[Black], Thin]], GraphicsComplex[mekhontsevWedgePoints, 
      Polygon[mekhontsevWedgeFaces]]}, Boxed -> False, Lighting -> "Neutral"]; 
  MekhontsevWedgeSubdivision[] := 
   Graphics3D[MapIndexed[{Directive[ColorData[97][Mod[First[#2] - 1, 8] + 1], Opacity[0.65]], 
       EdgeForm[Directive[LightDarkSwitched[Black], Thin]], GraphicsComplex[#1, 
        Polygon[mekhontsevWedgeFaces]]} & , mekhontsevWedgePieces], Boxed -> False, 
    Lighting -> "Neutral"]

Illustration

GraphicsRow[{MekhontsevWedge[], MekhontsevWedgeSubdivision[]}]