Project 3 Making other Surfaces

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Project 3 Making other Surfaces

• Davison CE High School for Girls
• 8Jf (Group 2)

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Project 3 Information

• OUR TASK!
• Look at our models
• Including the Tetrahedron, octahedron and
  icosahedron.
• Remember at each vertex the number of triangles
  must be the same.
• Explore various numbers of triangles at each
  vertex.

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What we did

• We explored the nrich website and investigated
  the subjects further.
• We began to form hyperbolic planes and joined
  them together- this was very confusing and
  complicated!
• We then tried this process with 6 triangles at
  the vertex.

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Making Hyperbolic Planes

• We made a large hyperbolic plane and then tried
  to connect it to make a Torus shape

• We found when we drew 1 straight lines on the
  hyperbolic planes we got 2 parallel lines

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Spheres

• We attempted to make a sphere out of Hexagons and
  Hyperbolic planes
• The hyperbolic planes werent working and some of
  us got fed up!
• The hexagons did work but it was hard to put them
  together!
• At the end we made a discovery

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Our discovery

• Some of us said
• Its like the triangulated hyperbolic plane,
  but is made using hexagons, with six at each
  vertex.
• If you draw a straight line it will complete
  a circle around the sphere.

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Hyperbolic plane

• We tried to make a Torus out of the hyperbolic
  plane, but we failed as we were short of polydron
  triangles.
• We also found it very complicated to ensure that
  there were seven triangles at each vertex.
• It was very flimsy and flexible, and kept
  breaking.

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Our discovery

• From as far as we got with the available
  triangles, we could see that eventually the
  triangles would join up to create a Torus.
  Unfortunately, we could not follow up this
  investigation.

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Hexagons- Donut

• We used the HEXAGONAL plane!!!!!!!!!!
• We made a donut shape using the hexagonal planes
• We tried to fill the gaps, but found that if we
  did, it would create only 4 at the vertex.(See
  arrow A)

Mmm Hexagonal Donuts!
A
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Evaluation

During our investigation we found that the
hyperbolic plane is hard to join together because
it very flimsy we then decided to try using a
hexagonal plane and this was much more
successful. Using this, we decided to investigate
the different shapes that we could form,
involving this method. After trying to make the
donut shape with the hyperbolic plane, we came to
the conclusion that the hexagonal plane makes
more shapes in less time due to the amount of
polydron at each vertex (it was not as flimsy).
We have found that the hexagons are easier to
work with.
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Thank you for watching our show