Editing Truncated icosidodecahedron (section)

== Dissection ==

The truncated icosidodecahedron is the [[convex hull]] of a [[rhombicosidodecahedron]] with [[cuboid]]s above its 30 squares, whose height to base ratio is {{math|[[golden ratio|φ]]}}. The rest of its space can be dissected into nonuniform cupolas, namely 12 [[pentagonal cupola|between inner pentagons and outer decagons]] and 20 [[triangular cupola|between inner triangles and outer hexagons]].

An alternative dissection also has a rhombicosidodecahedral core. It has 12 [[pentagonal rotunda]]e between inner pentagons and outer decagons. The remaining part is a [[toroidal polyhedron]].

{| class="wikitable collapsible"
! dissection images
|-
|
{{multiple image
 | align = left  | total_width = 650
 | image1 = Small in great rhombi 12-20, davinci small with cuboids.png |width1=1|height1=1 
 | image2 = Small in great rhombi 12-20, davinci.png
 | footer = These images show the rhombicosidodecahedron (violet) and the truncated icosidodecahedron (green). If their edge lengths are 1, the distance between corresponding squares is {{math|[[golden ratio|φ]]}}.
}}
[[File:Toroidal_excavated_truncated_Icosidodecahedron.gif|320px|thumb|right|The toroidal polyhedron remaining after the core and twelve rotundae are cut out]]
|}