D4.10 (EntityTopic, 15)

From Hi.gher. Space

Revision as of 22:43, 12 March 2014

D4.10 is a bilbirothawroid with a pair of antipodal tetrahedra surrounded by 6 bilunabirotundae (J91) each, with 4 tridiminished icosahedra filling up the gaps between the J91's around each tetrahedron. There are also 8 J92's, 4 on the two identical hemispheres of the polytope, which are oriented in dual orientation to each other.

It is related to D4.11 via a slight modification of its lace tower.

Elements

TODO: Split faces, edges and vertices into unique positions.

Cells

• 16 tetrahedra (2 + 6 + 8)
• 24 square pyramids
• 32 octahedra (24 + 8)
• 8 tridiminished icosahedra
• 8 triangular cupolas
• 24 pentagonal antiprisms
• 12 J91's
• 8 J92's

Faces

• 464 triangles
• 48 squares
• 72 pentagons
• 8 hexagons

• 636 edges
• 176 vertices

Lace tower

          x3o3o   // tetrahedron
          f3o3x   // 4 tetrahedra touching vertices of previous one
          o3x3f   // midpoints of J91's
          f3x3x   // square faces of J91's
          x3o3F   // octahedra above J63's
          x3F3o   // opposite edge of J91's
          f3x3f   // f3x vertices of 8 J92's (this is the midpoint)
          o3F3x
          F3o3x
          x3x3f
          f3x3o
          x3o3f
          o3o3x

As you can see, there are two antipodal tetrahedra. EDIT 3: Also, there are no lacing edges between f3x3x and x3o3F, so that part of the tower may be better written as:

           ...
           o3x3f
          /  f3x3x
      x3o3F    |   
         |    x3F3o
         | f3x3f |
         o3F3x   |
         |    F3o3x
        x3x3f   /
           f3x3o
          ...

Projections

Centered on one of the antipodal tetrahedra:

Same 4D viewpoint, with J92 cells highlighted:

Side-view, showing that it nearly has 16-cell symmetry:

Coordinates

apecs<1/√2, 1/√2, 1/√2> ~ <-(2*phi+3)/√2>
apecs<phi^2/√2, phi^2/√2, 1/(phi*√2)> ~ <-(phi+3)/√2>
apecs<(phi+2)/√2, phi/√2, -phi/√2> ~ <-(phi+2)/√2>
apecs<1/(phi*√2), phi^2/√2, (phi^2+2)/√2> ~ <-phi^2/√2>                                
apecs<-(phi+2)/√2, -phi/√2, -(phi+2)/√2> ~ <-phi/√2>
apecs<(2*phi+3)/√2, 1/√2, 1/√2> ~ <-1/√2>
apacs<0, phi*√2, phi^2*√2> ~ <0>
apecs<1/√2, 1/√2, -(2*phi+3)/√2> ~ <1/√2>
apecs<phi/√2, (phi+2)/√2, (phi+2)/√2> ~ <phi/√2>
apecs<1/(phi*√2), phi^2/√2, -(phi+3)/√2> ~ <phi^2/√2>
apecs<(phi+2)/√2, phi/√2, phi/√2> ~ <(phi+2)/√2>
apecs<1/(phi*√2), phi^2/√2, -phi^2/√2> ~ <(phi+3)/√2>
apecs<1/√2, 1/√2, -1/√2> ~ <(2*phi+3)/√2>

Software models

• Polyview .def file
• Stella4D .off file