Great grand 120-cell

Great grand 120-cell
Orthogonal projection
Type	Schläfli-Hess polytope
Cells	120 {5,5/2}
Faces	720 {5}
Edges	1200
Vertices	120
Vertex figure	{5/2,3}
Schläfli symbol	{5,5/2,3}
Coxeter-Dynkin diagram
Symmetry group	H₄, [3,3,5]
Dual	Great icosahedral 120-cell
Properties	Regular

In geometry, the great grand 120-cell or great grand polydodecahedron is a regular star 4-polytope with Schläfli symbol {5,5/2,3}. It is one of 10 regular Schläfli-Hess polytopes.

Related polytopes

It has the same edge arrangement as the small stellated 120-cell.

Orthographic projections by Coxeter planes
H₃	A₂ / B₃ / D₄	A₃ / B₂

References

Edmund Hess, (1883) Einleitung in die Lehre von der Kugelteilung mit besonderer Berücksichtigung ihrer Anwendung auf die Theorie der Gleichflächigen und der gleicheckigen Polyeder [1].
H. S. M. Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. ISBN 0-486-61480-8.
John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 26, Regular Star-polytopes, pp. 404–408)
Klitzing, Richard. "4D uniform polytopes (polychora) o3o5/2o5x - gaghi".

External links

Regular polychora Archived 2003-09-06 at the Wayback Machine
Discussion on names
Reguläre Polytope
The Regular Star Polychora

Regular 4-polytopes

Convex

5-cell	8-cell	16-cell	24-cell	120-cell	600-cell
{3,3,3} pentachoron 4-simplex	{4,3,3} tesseract 4-cube	{3,3,4} hexadecachoron 4-orthoplex	{3,4,3} icositetrachoron octaplex	{5,3,3} hecatonicosachoron dodecaplex	{3,3,5} hexacosichoron tetraplex

Star

icosahedral 120-cell	small stellated 120-cell	great 120-cell	grand 120-cell	great stellated 120-cell	grand stellated 120-cell	great grand 120-cell	great icosahedral 120-cell	grand 600-cell	great grand stellated 120-cell
{3,5,5/2} icosaplex	{5/2,5,3} stellated dodecaplex	{5,5/2,5} great dodecaplex	{5,3,5/2} grand dodecaplex	{5/2,3,5} great stellated dodecaplex	{5/2,5,5/2} grand stellated dodecaplex	{5,5/2,3} great grand dodecaplex	{3,5/2,5} great icosaplex	{3,3,5/2} grand tetraplex	{5/2,3,3} great grand stellated dodecaplex