The 9-sided Enneahedron - Numberphile

Comments · 391

• NU

  @numberphile · 1 year ago · pinned

  See the free trial from episode sponsor Brilliant - <a href="https://brilliant.org/numberphile">https://brilliant.org/numberphile</a>

  20

• PA

  @pandalonium · 1 year ago

  We’ve upgraded to 3D brown paper

  193

• SE

  @seancooper4058 · 1 year ago (edited)

  The shape sounds so complicated when all you can do is explain its properties, but then once it&apos;s finally constructed you find out that all along it was just 3 squares and 6 kites! Someone has probably made it by accident in the past! Amazing

  453

• AN

  @Android480 · 1 year ago

  He’s such a natural at this. He sounds like someone who’s been on the show for 10 years already. Absolutely brilliant, I’d love to see more of him.

  71

• SC

  @scoobyDrew247 · 1 year ago

  Christian was in my class in high school, we used to have competitions to see who could multiply big numbers together the fastest. Amazing to see him on Numberphile!

  49

• WO

  @woops9076 · 1 year ago

  Love the tiling jumper!

  293

• ER

  @erk2048 · 1 year ago

  Eulerian paths are taken on in the video about the bridges of Königsberg

  52

• GC

  @gcewing · 1 year ago

  Explanation of a cube for those that don&apos;t know what it is: It&apos;s like a tesseract but with only 3 dimensions.

  3

• CH

  @chrisgriffith1573 · 1 year ago (edited)

  I used this shape to make a &quot;stealthy&quot; looking spaceship model out of card stock. It&apos;s highly elongated, geometric, and now is about 30 years old. Completely a physical experimentation with flat shapes on a drafting table. I used to make models to draw them in illustrations. This one was so hard to draw due to the lack of angles that made 3D sense to whatever angle you placed it. No wonder these dimensional oddities have become the mainstay for stealth angularity.

  49

• EL

  @eliasmochan · 1 year ago

  I feel like it&apos;s not too well explained what the problem was. Given a polyhedral graph it&apos;s easy to construct a convex polyhedron with that graph as it&apos;s skeleton: just draw the graph on a sphere and take the convex hull of that. Their first solutions seems to be just that. What they wanted is for every symmetry of the graph to be a symmetry of the polyhedron. That&apos;s what makes the problem interesting.

  22

• TR

  @TristanFrodelius · 1 year ago

  Funny thing, I&apos;ve made this shape before, when designing dice shapes (in this case, intended as a D3). And yeah, it can&apos;t be drawn as a planar-graph/projection that maintains threefold symmetry without having a point at infinity; that&apos;s trivial to prove. Before this video finished, I paused and doodled the 3-fold graph (with the point at infinity), and then continued watching, to see the reveal of a shape I&apos;d seen before. &gt;w&lt; Shapes are friends to me. It&apos;s also very easy to create by modifying a truncated triangular bipyramid (that only has the 4-edge vertices truncated) into a rectified version instead. I&apos;m <i>genuinely</i> shocked this is considered new! I suppose more dilettantes ought to talk more about their hobbies! That hoodie kind of goes to show exactly that! :3

  17

• JT

  @JT-2357 · 1 year ago

  A simple way to construct an enneahedron (but not the one pictured in this video) is to intersect a triangular prism with a cube along its diagonal.

  2