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  "body": "\n## Description\n\nThe *120-cell* is the convex [[regular polytope|F60PD912D5]] in $\\R^4$ with [[Schläfli symbol|MAE6BF4DFK]] $\\set{5, 3, 3}$.\nIts cells are $120$ regular dodecahedra, three around each edge, and four cells meet at each vertex.\nIt has $600$ vertices, $1200$ edges, $720$ pentagonal faces and $120$ cells.\n\nCheck of the counts: each dodecahedron has $12$ pentagons, and each pentagon lies in exactly $2$ cells, so there are $120 \\cdot 12 / 2 = 720$ faces.\nEach pentagon has $5$ edges, and each edge lies in $3$ pentagons, so there are $720 \\cdot 5 / 3 = 1200$ edges.\nThe vertex figure is a regular tetrahedron $\\set{3,3}$, so each vertex lies on $4$ edges, and there are $1200 \\cdot 2 / 4 = 600$ vertices.\nThen $600 - 1200 + 720 - 120 = 0$, as Euler's relation for convex $4$-polytopes requires.\n\n## Remarks\n\nThe 120-cell is the dual of the [[600-cell|8MNQDK5X5W]].\nIts symmetry group is the reflection group $H_4$, of order $14400$.\nIt is the four-dimensional analogue of the regular dodecahedron $\\set{5, 3}$.\nThree dodecahedra fit around an edge with a small angular gap, since the dihedral angle of the dodecahedron is about $116.57^\\circ$.\n\n## Explanations\n\n### L1 human\n\nThe 120-cell is a four-dimensional solid made of $120$ regular dodecahedra.\nIt has $600$ corners, and it is the largest and most complicated of the six regular solids of four-dimensional space.\nIt plays the role in four dimensions that the dodecahedron plays in three.\n",
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