great ditrigonal icosidodecahedron

{{Short description|Polyhedron with 32 faces}}

{{Uniform polyhedra db|Uniform polyhedron stat table|gdID}}

File:Great ditrigonal icosidodecahedron.stl

In geometry, the great ditrigonal icosidodecahedron (or great ditrigonary icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U₄₇. It has 32 faces (20 triangles and 12 pentagons), 60 edges, and 20 vertices.{{Cite web|url=https://www.mathconsult.ch/static/unipoly/47.html|title=47: great ditrigonal icosidodecahedron|last=Maeder|first=Roman|date=|website=MathConsult|archive-url=|archive-date=|access-date=}} It has 4 Schwarz triangle equivalent constructions, for example Wythoff symbol 3 | 3 {{Frac|5|4}} gives Coxeter diagram {{CDD||label5-4|branch_10ru|split2|node}} = {{CDD|node_h3|5-2|node|3|node}}. It has extended Schläfli symbol a{{{Frac|5|2}},3} or c{3,{{Frac|5|2}}}, as an altered great stellated dodecahedron or converted great icosahedron.

Its circumradius is $\backslash frac\{\backslash sqrt\{3\}\}\{2\}$ times the length of its edge,{{Citation

| last = Weisstein | first = Eric W

| year = 2003

| title = CRC concise encyclopedia of mathematics

| isbn = 1-58488-347-2

| publisher = Chapman & Hall/CRC

| location = Boca Raton

}} a value it shares with the cube.