Tetrahedron (EntityTopic, 18)

From Hi.gher. Space

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*The [[planar]] [[cross-section]]s (''n'') of a tetrahedron are:
*The [[planar]] [[cross-section]]s (''n'') of a tetrahedron are:
<blockquote>''Unknown''</blockquote>
<blockquote>''Unknown''</blockquote>
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<br clear="all"><br>
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== Use ==
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Tetrahedral cells are found in these tetrashapes on FGwiki:
 +
*[[Hexacosichoron]] (600×, 100%)
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*[[Hexadecachoron]] (8×, 100%)
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*[[Pentachoron]] (5×, 100%)
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*[[Square dipyramid]] (4×, 67%)
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{{Trishapes}}
{{Trishapes}}
{{Rotope Nav|8|9|10|I'I<br>Triangular prism|<nowiki>I''</nowiki><br>Tetrahedron|(I'I)<br>Triangular torus|hedra}}
{{Rotope Nav|8|9|10|I'I<br>Triangular prism|<nowiki>I''</nowiki><br>Tetrahedron|(I'I)<br>Triangular torus|hedra}}
[[Category:Regular polyhedra]]
[[Category:Regular polyhedra]]

Revision as of 11:30, 22 September 2007

Template:Shape

A tetrahedron is a special case of a pyramid where the base is a triangle.

Equations

  • Variables:
l ⇒ length of edges of tetrahedron
  • All points (x, y, z) that lie on the surface of a tetrahedron will satisfy the following equations:
Unknown
  • All points (x, y, z) that lie on the edges of a tetrahedron will satisfy the following equations:
Unknown
total edge length = 6l
surface area = sqrt(3)l2
volume = 12-1sqrt(2)l3
  • The perpendicular height h of a tetrahedron is given by:
h = 3-1sqrt(6)l
Unknown

Use

Tetrahedral cells are found in these tetrashapes on FGwiki:


Notable Trishapes
Regular: tetrahedroncubeoctahedrondodecahedronicosahedron
Direct truncates: tetrahedral truncatecubic truncateoctahedral truncatedodecahedral truncateicosahedral truncate
Mesotruncates: stauromesohedronstauroperihedronstauropantohedronrhodomesohedronrhodoperihedronrhodopantohedron
Snubs: snub staurohedronsnub rhodohedron
Curved: spheretoruscylinderconefrustumcrind

Template:Rotope Nav