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  "body": "\n## Example\n\nTake a solid regular dodecahedron.\nGlue each face to the opposite face after a turn of $3/10$ of a full turn, that is, by the angle $3\\pi/5$.\nThe result is the Seifert–Weber space $W$, a closed orientable [[3-manifold|R20TB2KEQQ]].\n\nUnder these gluings, the $30$ edges of the dodecahedron fall into $6$ classes of $5$ edges, and all $20$ vertices become one point.\nThe cell structure has $1$ vertex, $6$ edges, $6$ faces and $1$ cell.\nSo its Euler characteristic is $1 - 6 + 6 - 1 = 0$, as it must be for a closed $3$-manifold.\nIn hyperbolic space $\\mathbb{H}^3$ there is a regular dodecahedron with dihedral angles $2\\pi/5$.\nWith this dodecahedron the $5$ angles around each edge class add up to $2\\pi$, and the gluing maps are isometries.\nSo $W$ is a closed [[hyperbolic 3-manifold|GHVW1Z35BS]].\n\n## Remarks\n\nIts first homology group is $(\\Z/5)^3$.\nGluing opposite faces with a turn of $1/10$ instead gives the [[Poincaré homology sphere|NHERCK7C43]], and a turn of $1/2$ gives the [[real projective space|1DDYB6VVSR]] $\\mathbb{RP}^3$.\nSeifert and Weber described the space in 1933; it was one of the first known closed hyperbolic $3$-manifolds.\n\n## Explanations\n\n### L1 human\n\nThe Seifert–Weber space is made from a dodecahedron, the solid with twelve pentagonal faces, by gluing opposite faces with a twist.\nIn ordinary space the corners do not fit together, but in hyperbolic space a large enough dodecahedron has smaller angles, and one size makes them exactly right.\nSo a hyperbolic creature living inside would see a perfect tiling of its space by dodecahedra.\n",
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