# Trigonic small stellated dodecahedron faceting

Trigonic small stellated dodecahedron faceting
Rank3
TypeOrbiform
Notation
Bowers style acronymTissidaf
Elements
Faces6 triangles, 6 pentagrams
Edges6+6+12
Vertices6+6
Vertex figures6 butterflies, edge lengths 1 and (5–1)/2
6 isosceles trapezoids, edge lengths 1, (5–1)/2, (5–1)/2, (5–1)/2
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {5-{\sqrt {5}}}{8}}}\approx 0.58779}$
Dihedral angles5/2–5/2: ${\displaystyle \arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }}$
3-5/2 #1: ${\displaystyle \arccos \left({\sqrt {\frac {5-2{\sqrt {5}}}{15}}}\right)\approx 79.18768^{\circ }}$
3-5/2 #2: ${\displaystyle \arccos \left({\sqrt {\frac {5+2{\sqrt {5}}}{15}}}\right)\approx 37.37737^{\circ }}$
Related polytopes
ArmyIke
ConjugateTrigonic great dodecahedron faceting
Convex hullIcosahedron, edge length (5–1)/2
Convex coreRhombohedron
Abstract & topological properties
Flag count96
Euler characteristic0
OrientableNo
Genus2
Properties
Symmetry(G2×A1)/2, order 12
ConvexNo
NatureTame

The trigonic small stellated dodecahedron faceting, or tissidaf, is an orbiform polyhedron and, as its name suggests, an edge faceting of the small stellated dodecahedron. Its faces are 6 triangles and 6 pentagrams.

It appears as a cell of the great trigonal swirlprism and the great toroidal trigonal swirlprism.

## Vertex coordinates

Its vertex coordinates are the same as those of the small stellated dodecahedron.