|
|
| Line 1: |
Line 1: |
| {{Even polygon db|Even polygon stat table|p30}}
| | Greetings. The writer's title is Phebe and she feels comfy when people use the full name. Since she was 18 she's been working as a receptionist but her marketing by no means comes. South Dakota is where me and my husband live. Body building is what my family members and I appreciate.<br><br>Here is my blog ... [http://www.missdica.com/a_gallery/1866456 at home std testing] |
| In [[geometry]], an '''triacontagon''' is a thirty-sided [[polygon]]. The sum of any triacontagon's interior angles is 5040 degrees.
| |
| | |
| One interior angle in a [[regular polygon|regular]] triacontagon is 168°, meaning that one exterior angle would be 12°. The triacontagon is the largest regular polygon whose interior angle is the sum of the interior angles of smaller polygons: 168° is the sum of the interior angles of the [[equilateral triangle]] (60°) and the [[regular pentagon]] (108°).
| |
| | |
| The regular triacontagon is a [[constructible polygon]], by an edge-[[bisection]] of a regular [[pentadecagon]], and can be seen as a [[Truncation (geometry)|truncated]] pentadecagon.
| |
| | |
| ==Area==
| |
| The [[area]] of a regular triacontangon is (with {{nowrap|''t'' {{=}} edge length}})
| |
| :<math>A = \frac{15}{2} t^2 \cot \frac{\pi}{30}</math>
| |
| | |
| ===Petrie polygons===
| |
| The regular triacontagon is the [[Petrie polygon]] for a number of higher dimensional polytopes with E<sub>8</sub> symmetry, shown in [[orthogonal projection]]s in the E<sub>8</sub> [[Coxeter plane]]:
| |
| | |
| {| class=wikitable
| |
| |- align=center valign=top
| |
| |[[File:4_21_t0_E8.svg|100px]]<BR>[[4 21 polytope|(4<sub>21</sub>)]]
| |
| |[[File:4_21_t1_E8.svg|100px]]<BR>[[Rectified 4 21 polytope|t<sub>1</sub>(4<sub>21</sub>)]]
| |
| |[[File:4_21_t2_E8.svg|100px]]<BR>t<sub>2</sub>(4<sub>21</sub>)
| |
| <!--|[[File:4_21_t3_E8.svg|100px]]<BR>t<sub>3</sub>(4<sub>21</sub>)-->
| |
| <!--|[[File:4_21_t4_E8.svg|100px]]<BR>t<sub>4</sub>(4<sub>21</sub>)-->
| |
| |[[File:2_41_t0_E8.svg|100px]]<BR>[[2_41 polytope|(2<sub>41</sub>)]]
| |
| |[[File:2_41_t1_E8.svg|100px]]<BR>[[Rectified 2_41 polytope|t<sub>1</sub>(2<sub>41</sub>)]]
| |
| <!--|[[File:1_42_t0_E8.svg|100px]]<BR>[[2_41 polytope|(1<sub>42</sub>)]]-->
| |
| |}
| |
| | |
| It is also the Petrie polygon for some higher dimensional polytopes with H<sub>4</sub> symmetry, shown in [[orthogonal projection]]s in the H<sub>4</sub> [[Coxeter plane]]:
| |
| | |
| {| class=wikitable
| |
| |- align=center valign=top
| |
| |[[File:120-cell graph H4.svg|100px]]<BR>[[120-cell]]
| |
| |[[File:120-cell_t1_H4.svg|100px]]<BR>[[Rectified 120-cell]]
| |
| |[[File:600-cell_t1_H4.svg|100px]]<BR>[[Rectified 600-cell]]
| |
| |[[File:600-cell graph H4.svg|100px]]<BR>[[600-cell]]
| |
| |}
| |
| | |
| ==References==
| |
| {{Reflist}}
| |
| *{{MathWorld|title=Triacontagon|urlname=Triacontagon}}
| |
| *[http://mathforum.org/dr.math/faq/faq.polygon.names.html Naming Polygons and Polyhedra]
| |
| | |
| {{Clear}}
| |
| {{polygons}}
| |
| | |
| [[Category:Polygons]]
| |
| | |
| {{Elementary-geometry-stub}}
| |
Greetings. The writer's title is Phebe and she feels comfy when people use the full name. Since she was 18 she's been working as a receptionist but her marketing by no means comes. South Dakota is where me and my husband live. Body building is what my family members and I appreciate.
Here is my blog ... at home std testing