Rhodomesohedral rotunda (EntityTopic, 15)
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- | The '''icosidodecahedral rotunda''' is a [[CRF polychoron]], [[ | + | The '''rhodomesohedral rotunda''', also known as the '''icosidodecahedral rotunda''', is a [[CRF polychoron]], [[rhodomesohedron]] || enlarged [[dodecahedron]] || [[truncated dodecahedron]]. Its cells are 1 rhodomesohedron, 12 [[pentagonal rotunda]]e, 40 [[tetrahedra]] and one truncated dodecahedron. |
+ | |||
+ | == History == | ||
+ | This polytope was discovered by [[Mrrl]] as one of the "offcuts" from diminishing the [[rectified 120-cell]]. | ||
+ | |||
+ | == Coordinates == | ||
+ | <φ+1, 0, 0, ±1> | ||
+ | <φ+1, 0, ±1, 0> | ||
+ | <φ+1, ±1, 0, 0> | ||
+ | |||
+ | <φ+1, ±(φ-1)/2, ±1/2, ±φ/2> | ||
+ | <φ+1, ±1/2, ±φ/2, ±(φ-1)/2> | ||
+ | <φ+1, ±φ/2, ±(φ-1)/2, ±1/2> | ||
+ | |||
+ | <φ+1/2, 0, ±(φ-1)/2, ±(φ+2)/2> | ||
+ | <φ+1/2, ±(φ-1)/2, ±(φ+2)/2, 0> | ||
+ | <φ+1/2, ±(φ+2)/2, 0, ±(φ-1)/2> | ||
+ | |||
+ | <φ+1/2, ±(φ-1)/2, ±φ/2, ±φ> | ||
+ | <φ+1/2, ±φ/2, ±φ, ±(φ-1)/2> | ||
+ | <φ+1/2, ±φ, ±(φ-1)/2, ±φ/2> | ||
+ | |||
+ | <φ+1/2, ±φ/2, ±1, ±(φ+1)/2> | ||
+ | <φ+1/2, ±1, ±(φ+1)/2, ±φ/2> | ||
+ | <φ+1/2, ±(φ+1)/2, ±φ/2, ±1> | ||
+ | |||
+ | <3φ/2, 0, ±1/2, ±(φ+1)/2> | ||
+ | <3φ/2, ±1/2, ±(φ+1)/2, 0> | ||
+ | <3φ/2, ±(φ+1)/2, 0, ±1/2> | ||
+ | |||
+ | <3φ/2, ±φ/2, ±φ/2, ±φ/2> | ||
+ | |||
+ | where φ = {{Over|1+√5|2}} is the [[golden ratio]]. | ||
== Additional images == | == Additional images == | ||
<[#box [id 15] [width 150] [height 210]]> | <[#box [id 15] [width 150] [height 210]]> | ||
+ | |||
+ | == Software models == | ||
+ | *[[Stella4D]] [http://hddb.teamikaria.com/dl/V146600PJV7287ASRPR5R439KN.off .off file] | ||
== External links == | == External links == | ||
*[http://hddb.teamikaria.com/forum/viewtopic.php?p=16694#p16694 Quickfur's original post] | *[http://hddb.teamikaria.com/forum/viewtopic.php?p=16694#p16694 Quickfur's original post] |
Latest revision as of 11:48, 15 March 2014
The rhodomesohedral rotunda, also known as the icosidodecahedral rotunda, is a CRF polychoron, rhodomesohedron || enlarged dodecahedron || truncated dodecahedron. Its cells are 1 rhodomesohedron, 12 pentagonal rotundae, 40 tetrahedra and one truncated dodecahedron.
History
This polytope was discovered by Mrrl as one of the "offcuts" from diminishing the rectified 120-cell.
Coordinates
<φ+1, 0, 0, ±1> <φ+1, 0, ±1, 0> <φ+1, ±1, 0, 0> <φ+1, ±(φ-1)/2, ±1/2, ±φ/2> <φ+1, ±1/2, ±φ/2, ±(φ-1)/2> <φ+1, ±φ/2, ±(φ-1)/2, ±1/2> <φ+1/2, 0, ±(φ-1)/2, ±(φ+2)/2> <φ+1/2, ±(φ-1)/2, ±(φ+2)/2, 0> <φ+1/2, ±(φ+2)/2, 0, ±(φ-1)/2> <φ+1/2, ±(φ-1)/2, ±φ/2, ±φ> <φ+1/2, ±φ/2, ±φ, ±(φ-1)/2> <φ+1/2, ±φ, ±(φ-1)/2, ±φ/2> <φ+1/2, ±φ/2, ±1, ±(φ+1)/2> <φ+1/2, ±1, ±(φ+1)/2, ±φ/2> <φ+1/2, ±(φ+1)/2, ±φ/2, ±1> <3φ/2, 0, ±1/2, ±(φ+1)/2> <3φ/2, ±1/2, ±(φ+1)/2, 0> <3φ/2, ±(φ+1)/2, 0, ±1/2> <3φ/2, ±φ/2, ±φ/2, ±φ/2>
where φ = 1+√5∕2 is the golden ratio.