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Table 1
18 3D flat spaces.
| Symbol | Name | Compact | Orientable | Homogeneous |
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|
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| E1 | 3-torus | yes | yes | yes |
| E2 | half-turn space | yes | yes | no |
| E3 | quarter-turn space | yes | yes | no |
| E4 | third-turn space | yes | yes | no |
| E5 | sixth-turn space | yes | yes | no |
| E6 | Hantzsche-Wendt space | yes | yes | no |
| E7 | Klein space | yes | no | no |
| E8 | Klein space with horizontal flip | yes | no | no |
| E9 | Klein space with vertical flip | yes | no | no |
| E10 | Klein space with half turn | yes | no | no |
| E11 | chimney space | no | yes | yes |
| E12 | chimney space with half turn | no | yes | no |
| E13 | chimney space with vertical flip | no | no | no |
| E14 | chimney space with horizontal flip | no | no | no |
| E15 | chimney space with half turn and flip | no | no | no |
| E16 | slab space | no | yes | yes |
| E17 | slab space with flip | no | no | no |
| E18 | simply connected space E3 | no | yes | yes |
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