Icosahedral truncate (EntityTopic, 11)

From Hi.gher. Space

(Difference between revisions)
m (K6.4 upgrade: img -> embed)
(polytope explorer integration)
Line 17: Line 17:
| bowers=Ti
| bowers=Ti
}}}}
}}}}
-
 
+
== Equations ==
-
== Geometry ==
+
-
=== Equations ===
+
*Variables:
*Variables:
<blockquote>''l'' ⇒ length of edges of the truncated icosahedron</blockquote>
<blockquote>''l'' ⇒ length of edges of the truncated icosahedron</blockquote>
Line 27: Line 25:
surface area = 3(3<sup>2<sup>-1</sup></sup>10+5<sup>2<sup>-1</sup></sup>(5+5<sup>2<sup>-1</sup></sup>2)<sup>2<sup>-1</sup></sup>)''l''<sup>2</sup><br>
surface area = 3(3<sup>2<sup>-1</sup></sup>10+5<sup>2<sup>-1</sup></sup>(5+5<sup>2<sup>-1</sup></sup>2)<sup>2<sup>-1</sup></sup>)''l''<sup>2</sup><br>
volume = (125+5<sup>2<sup>-1</sup></sup>43)''l''<sup>3</sup>4<sup>-1</sup></blockquote>
volume = (125+5<sup>2<sup>-1</sup></sup>43)''l''<sup>3</sup>4<sup>-1</sup></blockquote>
-
<br clear="all"><br>
+
 
 +
<[#polytope [id 24]]>
 +
 
{{Trishapes}}
{{Trishapes}}

Revision as of 22:19, 16 February 2014

Equations

  • Variables:
l ⇒ length of edges of the truncated icosahedron
total edge length = 90l
surface area = 3(32-110+52-1(5+52-12)2-1)l2
volume = (125+52-143)l34-1

Incidence matrix

Dual: pentakis dodecahedron

#TXIDVaEaEb5a6aTypeName
0 Va = point ;
1 Ea 2 = digon ;
2 Eb 2 = digon ;
3 5a 505 = pentagon ;
4 6a 633 = hexagon ;
5 C1a 6030601220 = truncated icosahedron ;

Usage as facets


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