Message Boards Message Boards

GROUPS:

Seven Triangle Octahedron

Posted 2 years ago
3021 Views
|
1 Reply
|
3 Total Likes
|

Take a strip of 7 triangles, tape the edges of the end triangles together, and fold it to make an octahedron.

seven triangles

Row[Table[Graphics[{ Line[{ {Sqrt[3], 1}, {0, 2}, {Sqrt[3], 3}, {0, 4}, {Sqrt[3], 5}, {0, 6}, {Sqrt[3], 7}, {0, 8}, {0, 0}, {Sqrt[3], 1}, {Sqrt[3], 7} }]}, ImageSize -> {173, 800} .9], {4}]]

Consider the following set of points:

triloop2 = {{{6, 2, 2}, {5, 1, 6}, {6, 5, 5}}, {{6, 2, 2}, {3, 2, 5}, {6, 5, 5}}, {{3, 2, 5}, {3, 5, 2}, {6, 2, 2}}, {{2, 1, 3}, {6, 2, 2}, {3, 5, 2}}, {{2, 4, 6}, {3, 5, 2}, {2, 1, 3}}, {{5, 1, 6}, {2, 4, 6}, {2, 1, 3}}, {{5, 1, 6}, {2, 4, 6}, {6, 5, 5} }};  
triloop4 = {{{9, 39, 12}, {18, 48, 30}, {12, 24, 36}}, {{9, 39, 12}, {29, 41, 22}, {12, 24, 36}}, {{29, 41, 22}, {27, 21, 12}, {9, 39, 12}}, {{33, 45, 6}, {9, 39, 12}, {27, 21, 12}}, {{36, 30, 30}, {27, 21, 12}, {33, 45, 6}}, {{18, 48, 30}, {36, 30, 30}, {33, 45, 6}}, {{18, 48, 30}, {36, 30, 30}, {12, 24, 36}}}/6;

That set of triangles gives the solution. It's a combination of an octahedron and a tetrahedron. The tetrahedron point touches the center of the opposite point.

Graphics3D[{ Polygon /@ triloop2}, SphericalRegion -> True, Boxed -> False, ImageSize -> {600, 600}] 

seven triangle octahedron

Curiously, two of these can be put together so that the bottom triangles have edge to edge contact.

Graphics3D[{ Polygon /@ triloop2, Polygon /@ triloop4}, 
 SphericalRegion -> True, Boxed -> False, ImageSize -> {600, 600}]

two seven octahedron

enter image description here - another post of yours has been selected for the Staff Picks group, congratulations! We are happy to see you at the top of the "Featured Contributor" board. Thank you for your wonderful contributions, and please keep them coming!

Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Reply Preview
Attachments
Remove
or Discard

Group Abstract Group Abstract