4.1. Shape’s references¶
| Vertices | Label | Shape | Symmetry |
|---|---|---|---|
| 2 | L-2 | Linear | D∞h |
| vT-2 | Divacant tetrahedron (V-shape, 109.47°) | C2v | |
| vOC-2 | Tetravacant octahedron (L-shape, 90.47°) | C2v | |
| 3 | TP-3 | Trigonal planar | D3h |
| vT-3 | Pyramid‡ (vacant tetrahedron) | C3v | |
| fac-vOC-3 | fac-Trivacant octahedron | C3v | |
| mer-vOC-3 | mer-Trivacant octahedron (T-shape) | C2v | |
| 4 | SP-4 | Square | D4h |
| T-4 | Tetrahedron | Td | |
| SS-4 | Seesaw or sawhorse ‡ (cis-divacant octahedron) | C2v | |
| vTBPY-4 | Axially vacant trigonal bipyramid | C3v | |
| 5 | PP-5 | Pentagon | D5h |
| vOC-5 | Vacant octahedron ‡ (Johnson square pyramid, J1) | C4v | |
| TBPY-5 | Trigonal bipyramid | D3h | |
| SPY-5 | Square pyramid § | C4v | |
| JTBPY-5 | Johnson trigonal bipyramid (J12) | D3h | |
| 6 | HP-6 | Hexagon | D6h |
| PPY-6 | Pentagonal pyramid | C5v | |
| OC-6 | Octahedron | Oh | |
| TPR-6 | Trigonal prism | D3h | |
| JPPY-6 | Johnson pentagonal pyramid (J2) | C5v | |
| 7 | HP-7 | Heptagon | D7h |
| HPY-7 | Hexagonal pyramid | C6v | |
| PBPY-7 | Pentagonal bipyramid | D5h | |
| COC-7 | Capped octahedron * | C3v | |
| CTPR-7 | Capped trigonal prism * | C2v | |
| JPBPY-7 | Johnson pentagonal bipyramid (J13) | D5h | |
| JETPY-7 | Elongated triangular pyramid (J7) | C3v | |
| 8 | OP-8 | Octagon | D8h |
| HPY-8 | Heptagonal pyramid | C7v | |
| HBPY-8 | Hexagonal bipyramid | D6h | |
| CU-8 | Cube | Oh | |
| SAPR-8 | Square antiprism | D4d | |
| TDD-8 | Triangular dodecahedron | D2d | |
| JGBF-8 | Johnson - Gyrobifastigium (J26) | D2d | |
| JETBPY-8 | Johnson - Elongated triangular bipyramid (J14) | D3h | |
| JBTP-8 | Johnson - Biaugmented trigonal prism (J50) | C2v | |
| BTPR-8 | Biaugmented trigonal prism | C2v | |
| JSD-8 | Snub disphenoid (J84) | D2d | |
| TT-8 | Triakis tetrahedron | Td | |
| ETBPY-8 | Elongated trigonal bipyramid (see 8) | D3h | |
| 9 | EP-9 | Enneagon | D9h |
| OPY-9 | Octagonal pyramid | C8v | |
| HBPY-9 | Heptagonal bipyramid | D7h | |
| JTC-9 | Triangular cupola (J3) = trivacant cuboctahedron | C3v | |
| JCCU-9 | Capped cube (Elongated square pyramid, J8) | C4v | |
| CCU-9 | Capped cube | C4v | |
| JCSAPR-9 | Capped sq. antiprism (Gyroelongated square pyramid J10) | C4v | |
| CSAPR-9 | Capped square antiprism | C4v | |
| JTCTPR-9 | Tricapped trigonal prism (J51) | D3h | |
| TCTPR-9 | Tricapped trigonal prism | D3h | |
| JTDIC-9 | Tridiminished icosahedron (J63) | C3v | |
| HH-9 | Hula-hoop | C2v | |
| MFF-9 | Muffin | Cs | |
| 10 | DP-10 | Decagon | D10h |
| EPY-10 | Enneagonal pyramid | C9v | |
| OBPY-10 | Octagonal bipyramid | D8h | |
| PPR-10 | Pentagonal prism | D5h | |
| PAPR-10 | Pentagonal antiprism | D5d | |
| JBCCU-10 | Bicapped cube (Elongated square bipyramid J15) | D4h | |
| JBCSAPR-10 | Bicapped square antiprism (Gyroelongated square bipyramid J17) | D4d | |
| JMBIC-10 | Metabidiminished icosahedron (J62) | C2v | |
| JATDI-10 | Augmented tridiminished icosahedron (J64) | C3v | |
| JSPC-10 | Sphenocorona (J87) | C2v | |
| SDD-10 | Staggered dodecahedron (2:6:2) # | D2 | |
| TD-10 | Tetradecahedron (2:6:2) | C2v | |
| HD-10 | Hexadecahedron (2:6:2, or 1:4:4:1) | D4h | |
| 11 | HP-11 | Hendecagon | D11h |
| DPY-11 | Decagonal pyramid | C10v | |
| EBPY-11 | Enneagonal bipyramid | D9h | |
| JCPPR-11 | Capped pent. Prism (Elongated pentagonal pyramid J9) | C5v | |
| JCPAPR-11 | Capped pent. antiprism (Gyroelongated pentagonal pyramid J11) | C5v | |
| JaPPR-11 | Augmented pentagonal prism (J52) | C2v | |
| JASPC-11 | Augmented sphenocorona (J87) | Cs | |
| 12 | DP-12 | Dodecagon | D12h |
| HPY-12 | Hendecagonal pyramid | C11v | |
| DBPY-12 | Decagonal bipyramid | D10h | |
| HPR-12 | Hexagonal prism | D6h | |
| HAPR-12 | Hexagonal antiprism | D6d | |
| TT-12 | Truncated tetrahedron | Td | |
| COC-12 | Cuboctahedron | Oh | |
| ACOC-12 | Anticuboctahedron (Triangular orthobicupola J27) | D3h | |
| IC-12 | Icosahedron | Ih | |
| JSC-12 | Square cupola (J4) | C4v | |
| JEPBPY-12 | Elongated pentagonal bipyramid (J16) | D6h | |
| JBAPPR-12 | Biaugmented pentagonal prism (J53) | C2v | |
| JSPMC-12 | Sphenomegacorona (J88) | Cs | |
| 20 | DD-20 | Dodecahedron † | Ih |
| 24 | TCU-24 | Truncated cube | Oh |
| TOC-24 | Truncated octahedron | Oh | |
| 48 | TCOC-48 | Truncated cuboctahedron | Oh |
| 60 | TRIC-60 | Truncated icosahedron (fullerene) | Ih |
* Non regular polyhedron, for definition of reference shape see references above.
‡ A regular polyhedron with one or two vertices removed.
§ Spherical distribution of vertices with mass center at the origin (apical-basal bond angles of 104.45°).
† For polyhedra with more than 12 vertices the calculation times may be unpractical, for now avoid this calculations
an upgrade is comming soon.
# This is a chiral polyhedron. It must be noticed that the algorithm used by Shape does not distinguish
the two enantiomers of a chiral shape. Therefore, whenever a chiral reference polyhedron is used, the resulting shape
measures may not refer to that specific polyhedron but to its enantiomer.