3D lattice of a tetrahedron. What is it called?

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











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I recently stumbled on this image and have been looking for a name for it:



pyramid image http://tetraktys.de/bilder/buckminster-tetraeder.gif



It’s not a Seirpinski pyramid because it doesn’t become fractal, it’s just a subdivision of the original pyramid. Any ideas?






geometry euclidean-geometry complex-geometry geometric-topology







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  • you can tile space with a combination of octahedra and tetrahedra. That's what they are showing.
    – Will Jagy
    Aug 31 at 4:34










  • If scaled in the most convenient manner, the centers of the regular octahedra occur at integer points $(x,y,z)$ where $x+y+z$ is even.
    – Will Jagy
    Aug 31 at 4:38














up vote
0
down vote

favorite












I recently stumbled on this image and have been looking for a name for it:



pyramid image http://tetraktys.de/bilder/buckminster-tetraeder.gif



It’s not a Seirpinski pyramid because it doesn’t become fractal, it’s just a subdivision of the original pyramid. Any ideas?






geometry euclidean-geometry complex-geometry geometric-topology







share|cite|improve this question























  • you can tile space with a combination of octahedra and tetrahedra. That's what they are showing.
    – Will Jagy
    Aug 31 at 4:34










  • If scaled in the most convenient manner, the centers of the regular octahedra occur at integer points $(x,y,z)$ where $x+y+z$ is even.
    – Will Jagy
    Aug 31 at 4:38












up vote
0
down vote

favorite









up vote
0
down vote

favorite











I recently stumbled on this image and have been looking for a name for it:



pyramid image http://tetraktys.de/bilder/buckminster-tetraeder.gif



It’s not a Seirpinski pyramid because it doesn’t become fractal, it’s just a subdivision of the original pyramid. Any ideas?






geometry euclidean-geometry complex-geometry geometric-topology







share|cite|improve this question















I recently stumbled on this image and have been looking for a name for it:



pyramid image http://tetraktys.de/bilder/buckminster-tetraeder.gif



It’s not a Seirpinski pyramid because it doesn’t become fractal, it’s just a subdivision of the original pyramid. Any ideas?






geometry euclidean-geometry complex-geometry geometric-topology




geometry euclidean-geometry complex-geometry geometric-topology






share|cite|improve this question















share|cite|improve this question













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edited Aug 31 at 11:37









MJD

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46.2k28199378










asked Aug 31 at 4:22









Michael Payne

11




11











  • you can tile space with a combination of octahedra and tetrahedra. That's what they are showing.
    – Will Jagy
    Aug 31 at 4:34










  • If scaled in the most convenient manner, the centers of the regular octahedra occur at integer points $(x,y,z)$ where $x+y+z$ is even.
    – Will Jagy
    Aug 31 at 4:38
















  • you can tile space with a combination of octahedra and tetrahedra. That's what they are showing.
    – Will Jagy
    Aug 31 at 4:34










  • If scaled in the most convenient manner, the centers of the regular octahedra occur at integer points $(x,y,z)$ where $x+y+z$ is even.
    – Will Jagy
    Aug 31 at 4:38















you can tile space with a combination of octahedra and tetrahedra. That's what they are showing.
– Will Jagy
Aug 31 at 4:34




you can tile space with a combination of octahedra and tetrahedra. That's what they are showing.
– Will Jagy
Aug 31 at 4:34












If scaled in the most convenient manner, the centers of the regular octahedra occur at integer points $(x,y,z)$ where $x+y+z$ is even.
– Will Jagy
Aug 31 at 4:38




If scaled in the most convenient manner, the centers of the regular octahedra occur at integer points $(x,y,z)$ where $x+y+z$ is even.
– Will Jagy
Aug 31 at 4:38










1 Answer
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This is the tetrahedral-octahedral honeycomb. A honeycomb is the three-dimensional analog of a tiling.



It's also called the face-centered cubic lattice because the vertices lie at the vertices of a simple cubic lattice, plus also at the centers of the faces of the cubes. (But not at the centers of the cubes themselves.) This ties in with Will Jagy's comment about the vertices being at points where $x+y+z$ is an even integer.



If you stack up spheres in the obvious way (the way they make pyramids of oranges and apples in the supermarket) the centers of the spheres lie at the vertices of this honeycomb.






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    1 Answer
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    active

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    1 Answer
    1






    active

    oldest

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    active

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    up vote
    4
    down vote



    accepted










    This is the tetrahedral-octahedral honeycomb. A honeycomb is the three-dimensional analog of a tiling.



    It's also called the face-centered cubic lattice because the vertices lie at the vertices of a simple cubic lattice, plus also at the centers of the faces of the cubes. (But not at the centers of the cubes themselves.) This ties in with Will Jagy's comment about the vertices being at points where $x+y+z$ is an even integer.



    If you stack up spheres in the obvious way (the way they make pyramids of oranges and apples in the supermarket) the centers of the spheres lie at the vertices of this honeycomb.






    share|cite|improve this answer


























      up vote
      4
      down vote



      accepted










      This is the tetrahedral-octahedral honeycomb. A honeycomb is the three-dimensional analog of a tiling.



      It's also called the face-centered cubic lattice because the vertices lie at the vertices of a simple cubic lattice, plus also at the centers of the faces of the cubes. (But not at the centers of the cubes themselves.) This ties in with Will Jagy's comment about the vertices being at points where $x+y+z$ is an even integer.



      If you stack up spheres in the obvious way (the way they make pyramids of oranges and apples in the supermarket) the centers of the spheres lie at the vertices of this honeycomb.






      share|cite|improve this answer
























        up vote
        4
        down vote



        accepted







        up vote
        4
        down vote



        accepted






        This is the tetrahedral-octahedral honeycomb. A honeycomb is the three-dimensional analog of a tiling.



        It's also called the face-centered cubic lattice because the vertices lie at the vertices of a simple cubic lattice, plus also at the centers of the faces of the cubes. (But not at the centers of the cubes themselves.) This ties in with Will Jagy's comment about the vertices being at points where $x+y+z$ is an even integer.



        If you stack up spheres in the obvious way (the way they make pyramids of oranges and apples in the supermarket) the centers of the spheres lie at the vertices of this honeycomb.






        share|cite|improve this answer














        This is the tetrahedral-octahedral honeycomb. A honeycomb is the three-dimensional analog of a tiling.



        It's also called the face-centered cubic lattice because the vertices lie at the vertices of a simple cubic lattice, plus also at the centers of the faces of the cubes. (But not at the centers of the cubes themselves.) This ties in with Will Jagy's comment about the vertices being at points where $x+y+z$ is an even integer.



        If you stack up spheres in the obvious way (the way they make pyramids of oranges and apples in the supermarket) the centers of the spheres lie at the vertices of this honeycomb.







        share|cite|improve this answer














        share|cite|improve this answer



        share|cite|improve this answer








        edited Aug 31 at 5:35


























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