The Tetrahedron
The Tetrahedron at a Glance:
| Number of faces: |
4 triangles |
| Number of edges: |
6 |
| Number of vertices: |
4 |
| Dihedral angle: |
70’32″ |
| Facial angle: |
60′ |
| Central angle: |
109’28″ |
| Elemental attribution: |
Fire |
| Geometric dual: |
tetrahedron |
Imaging the Tetrahedron:
small, basic animation (poorer quality, shorter download)
(IMAGE REMOVED)
larger, more complex animation (higher quality, longer download)
(IMAGE REMOVED)
ancient celtic model of the tetrahedron, carved in stone
an artist’s conceptualization of the tetrahedron
net, or pattern, that can be used to create a tetrahedron from cardstock
Proportions within the Tetrahedron
Proportions relative to edge length (if edge length equals one)
|
Insphere |
Interspere |
Circumsphere |
Surface Area |
|
0.204124145 |
0.353553391 |
0.612372436 |
|
|
|
square root of 2 divided by 4 |
|
|
Proportions relative to insphere (if insphere radius equals one)
|
Edge Length |
Intersphere |
Circumsphere |
Surface Area |
|
4.898979486 |
1.732050808 |
3 |
|
|
|
square root of 3 |
|
|
Proportions relative to intersphere (if intersphere radius equals one)
|
Edge Length |
Insphere |
Circumsphere |
Surface Area |
|
2.828427125 |
0.577350269 |
1.732050808 |
|
|
8 times (the square root of 2 divided by 4) |
1 divided by the square root of 3 |
square root of 3 |
|
Proportions relative to circumsphere
(if circumsphere radius equals one)
|
Edge Length |
Insphere |
Intersphere |
Surface Area |
|
1.632993162 |
0.33333333 |
0.577350269 |
|
|
|
1 divided by 3 |
1 divided by the square root of 3 |
|
Special thanks to Bruce
Rawles for supplying the above listed proportional figures.
all materials copyright 2010, Aidrian O'Connor
3 Responses to “The Tetrahedron”
neat stuff, cheers man
What aout the volumes of the platonic solids the their respective edge lengths. Do you have an equation for that? I am quite curious. Thank you for all the info.
Joof – I worked out the above equations by looking at an awesome chart by Bruce Rawles, many many years ago. I just found it again – awesome that he still has it posted: http://www.geometrycode.com/free/polyhedra-math-tables-for-platonic-and-archimedean-solids/
I worked the above out by making a spreadsheet that had many many permutations of multiplying the sqrt2, sqrt3, and phi by each other, dividing them, multiplying them, creating exponential values… and then I just methodically compared the results to Bruce’s table. It was pretty amazing to discover all the places that these values appeared.
Bruce would probably be the guy to ask… he’s a mathematician… I’m a hack.
Thanks for your comment – Aidrian
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