# Trigonic great dodecahedron faceting

Trigonic great dodecahedron faceting
Rank3
TypeOrbiform
Notation
Bowers style acronymTigdaf
Elements
Faces6 triangles, 6 pentagons
Edges6+6+12
Vertices6+6
Vertex figures6 butterflies, edge lengths 1 and (1+5)/2
6 crossed isosceles trapezoids, edge lengths 1, (1+5)/2, (1+5)/2, (1+5)/2
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {5+{\sqrt {5}}}{8}}}\approx 0.95106}$
Dihedral angles3-5 #1: ${\displaystyle \arccos \left(-{\sqrt {\frac {5-2{\sqrt {5}}}{15}}}\right)\approx 100.81232^{\circ }}$
5-5: ${\displaystyle \arccos \left({\frac {\sqrt {5}}{5}}\right)\approx 63.43495^{\circ }}$
3-5 #2: ${\displaystyle \arccos \left({\sqrt {\frac {5+2{\sqrt {5}}}{15}}}\right)\approx 37.37737^{\circ }}$
Number of external pieces30
Level of complexity16
Related polytopes
ArmyIke
ConjugateTrigonic small stellated dodecahedron faceting
Convex hullIcosahedron
Convex coreObtuse golden rhombohedron, edge length 1
Abstract & topological properties
Flag count96
Euler characteristic0
OrientableNo
Genus2
Properties
Symmetry(G2×A1)/2, order 12
ConvexNo
NatureTame

The trigonic great dodecahedron faceting or tigdaf, also known as the accordion, is an orbiform polyhedron and an edge faceting of the icosahedron. Its faces are 6 triangles and 6 pentagons.

It appears as a cell of the small trigonal swirlprism.

## Vertex coordinates

Its vertex coordinates are the same as those of the icosahedron.