.. highlight:: rst .. _shape_references: .. |D2| replace:: D\ :sub:`2` .. |Dih| replace:: D\ :sub:`∞h` .. |D3h| replace:: D\ :sub:`3h` .. |D4h| replace:: D\ :sub:`4h` .. |D5h| replace:: D\ :sub:`5h` .. |D6h| replace:: D\ :sub:`6h` .. |D7h| replace:: D\ :sub:`7h` .. |D8h| replace:: D\ :sub:`8h` .. |D9h| replace:: D\ :sub:`9h` .. |D10h| replace:: D\ :sub:`10h` .. |D11h| replace:: D\ :sub:`11h` .. |D12h| replace:: D\ :sub:`12h` .. |D2d| replace:: D\ :sub:`2d` .. |D4d| replace:: D\ :sub:`4d` .. |D5d| replace:: D\ :sub:`5d` .. |D6d| replace:: D\ :sub:`6d` .. |Cs| replace:: C\ :sub:`s` .. |C2v| replace:: C\ :sub:`2v` .. |C3v| replace:: C\ :sub:`3v` .. |C4v| replace:: C\ :sub:`4v` .. |C5v| replace:: C\ :sub:`5v` .. |C6v| replace:: C\ :sub:`6v` .. |C7v| replace:: C\ :sub:`7v` .. |C8v| replace:: C\ :sub:`8v` .. |C9v| replace:: C\ :sub:`9v` .. |C10v| replace:: C\ :sub:`10v` .. |C11v| replace:: C\ :sub:`11v` .. |Td| replace:: T\ :sub:`d` .. |Oh| replace:: O\ :sub:`h` .. |Ih| replace:: I\ :sub:`h` +---------+------------+------------------------------------------------------------------+----------+ | Vertices| Label | Shape | Symmetry | +=========+============+==================================================================+==========+ | 2 | L-2 | Linear | |Dih| | + +------------+------------------------------------------------------------------+----------+ | | vT-2 | Divacant tetrahedron (V-shape, 109.47°) | |C2v| | + +------------+------------------------------------------------------------------+----------+ | | vOC-2 | Tetravacant octahedron (L-shape, 90.00°) | |C2v| | +---------+------------+------------------------------------------------------------------+----------+ | 3 | TP-3 | Trigonal planar | |D3h| | + +------------+------------------------------------------------------------------+----------+ | | vT-3 | Pyramid\ :sup:`b`\ (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\ :sup:`b`\ (cis-divacant octahedron) | |C2v| | + +------------+------------------------------------------------------------------+----------+ | | vTBPY-4 | Axially vacant trigonal bipyramid | |C3v| | +---------+------------+------------------------------------------------------------------+----------+ | 5 | PP-5 | Pentagon | |D5h| | + +------------+------------------------------------------------------------------+----------+ | | vOC-5 | Vacant octahedron\ :sup:`b`\ (Johnson square pyramid, J1) | |C4v| | + +------------+------------------------------------------------------------------+----------+ | | TBPY-5 | Trigonal bipyramid | |D3h| | + +------------+------------------------------------------------------------------+----------+ | | SPY-5 | Square pyramid\ :sup:`c`\ | |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\ :sup:`a`\ | |C3v| | + +------------+------------------------------------------------------------------+----------+ | | CTPR-7 | Capped trigonal prism\ :sup:`a`\ | |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)\ :sup:`e`\ | |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\ :sup:`d`\ | |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| | +---------+------------+------------------------------------------------------------------+----------+ | a Non regular polyhedron. | b A regular polyhedron with one or two vertices removed. | c Spherical distribution of vertices with mass center at the origin (apical-basal bond angles of 104.45°). | d For polyhedra with more than 12 vertices the calculation times may be unpractical, for now avoid this calculations an upgrade is comming soon. | e 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.