About 90% of CTC cubics are circumcubics. These few do NOT pass through the A-vertex of ABC.

Knnn NOT through the A-vertex of ABC |
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Not through A of ABC (TCCT 6.1): K038, K048, K051, K075, K076, K077, K078, K079, K083B, K083C, K100, K138, K143B, K143C, K144, K153, K193, K203, K215, K219, K226, K244, K258, K265, K266, K271, K272, K277, K369, K401, K417, K418, K437, K456A, K458, K459, K460, K461, K462, K463, K508, K509, K511, K583, K591, K592, K593, K598, K600, K609, K645, K648, K649, K650, K651, K652, K656, K666, K667, K687, K700, K703, K722, K723, K725, K726, K727, K728, K733, K735, K736, K742, K752, K753, K758, K764, K765, K793, K794, K795, K796 |

Triangle: Knnn through its A-vertex |
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excentral (TCCT 6.7): K001, K002, K003, K004, K005, K006, K020, K021, K029, K030, K031, K035, K077, K078, K100, K102, K109, K128, K129a, K129b, K130, K152, K156, K158, K169, K173, K227A, K227B, K227C, K243, K258, K269, K270, K282, K316, K326, K343, K351, K364, K410, K414, K417, K422, K423, K424a, K424b, K434, K456A, K456B, K456C, K502, K585, K609, K655, K661, K668, K692, K695, K704, K717, K742, K751, K763 |

medial (TCCT 6.2): K002, K009, K026, K038, K043, K051, K143A, K168, K177, K203, K207, K208, K219, K220, K226, K237, K251, K252, K253, K258, K259, K260, K265, K277, K284, K307, K321, K341a, K341b, K345, K357, K363, K376, K426, K446, K453, K472, K485, K489, K512, K557, K559, K564, K565, K567, K569, K570, K607, K612, K637, K663, K671, K752 |

anticomplementary (TCCT 6.3): K007, K008, K034, K045, K080, K083A, K092, K133, K141, K142, K143A, K143B, K143C, K144, K146, K154, K170, K200, K210, K211, K235, K240, K242, K254, K264a, K264b, K279, K311, K355, K371, K377, K425, K449, K455, K548, K605, K610, K611, K617, K659, K753 |

orthic (TCCT 6.4): K006, K044, K049, K050, K051, K053A, K059, K110A, K170, K176, K181, K182, K209, K212, K233, K238, K329, K334, K337, K339, K350, K391, K415, K416, K429, K445, K475, K496, K517, K591, K691, K709, K718, K742 |

tangential (TCCT 6.5): K075, K076, K108, K160, K161, K171, K172, K174, K175, K176, K177, K178, K179, K180, K236, K312, K389, K405, K428, K430, K431, K432, K478, K495, K622 |

Thomson (CTC K002): K002, K078, K138, K167, K172, K280, K297, K463, K581, K609, K615, K624, K625, K626, K703, K727, K758, K759, K760, K761, K764, K765 |

symmedial (MathWorld): K102, K167, K215, K346, K367, K368, K390, K444, K579, K629, K659, K673, K693, K739, K790 |

intouch / Gergonne(TCCT 6.8): K333, K360, K365, K561, K571, K572, K573, K574, K575, K577, K578, K631, K666, K713, K747 |

incentral (TCCT 6.6): K097, K101, K157, K175, K206, K215, K362, K511, K560, K632, K672, K749, K761, K770, K774 |

circumtangential (TCCT 6.28): K024, K078, K085, K098, K105, K403, K409, K686, K723, K726, K727, K728, K734, K735 |

first Brocard (CTC): K012, K017, K020, K153, K512, K545, K547, K548, K549, K550, K551, K552, K553 |

circumnormal (TCCT 6.29): K003, K009, K227A, K361, K373, K404, K405, K519, K664, K725, K735, K736 |

ABC reflected about O (TCCT 6.12): K004, K047, K069, K080, K426, K443, K566, K703, K706, K712 |

reflection A in BC: K001, K032, K115, K116, K117, K118, K119, K120, K216 |

MacBeath (MathWorld): K028, K045, K555, K556, K562, K563, K583, K647, K674 |

Grebe (CTC K102): K102, K138, K177, K281, K642, K643, K644, K729, K731 |

extouch (TCCT 6.9): K033, K199, K200, K308, K338, K667, K692, K710 |

second Brocard (CTC): K018, K022, K053A, K083A, K509, K538, K793 |

cuspes of Steiner deltoid (see CTC Q000) / 1st Steiner equilateral (see ETC X(6070)): K071, K244, K648, K649, K650, K651, K652 |

Carnot / Johnson (reflection of ABC about X(5). MathWorld): K026, K044, K465, K526, K562, K725 |

third Brocard (CTC): K017, K020, K444, K546, K549 |

Steiner (MathWorld): K035, K242, K403, K568, K602 |

Schroeter (see ETC X(8286): K079, K237, K238, K239, K672 |

excentral of Thomson (CTC Q113): K078, K615, K763, K764, K765 |

second Conway (see ETC X(9776)): K007, K028, K461, K651 |

orthocentroidal (see ETC X(5476)): K005, K295, K397, K733 |

half altitude (TCCT 6.38): K002, K122, K645, K752 |

Steiner Deltoid NP touches (see CTC Q000) / 2nd Steiner equilateral (see ETC X6070)): K412, K583, K722 |

second circumperp (TCCT 6.22): K100, K318, K561 |

outer Napoleon (TCCT 6.31): K005, K463, K733 |

inner Napoleon (TCCT 6.32): K005, K463, K733 |

hexyl (TCCT 6.36): K004, K100, K736 |

first Morley (TCCT 6.25): K029, K227A, K584 |

first Morley adjunct (TCCT 6.30): K029, K227A, K584 |

circum-orthic (TCCT 6.20): K110A, K158, K580 |

third Morley (TCCT 6.27): K030, K227A |

third Morley adjunct (MathWorld): K030, K227A |

second Morley (TCCT 6.26): K031, K227A |

second Morley adjunct (MathWorld): K031, K227A |

reflected 1st Brocard(CTC table 32): K020, K797 |

medial of Thomson: K758, K765 |

Johnson (Quim Castellsaguer): K018, K539 |

isogonal of reflected 1st Brocard(CTC table 32): K020, K797 |

inner Garcia (see ETC X(5587)): K456A, K679 |

Fuhrmann (TCCT 8.25): K028, K680 |

fourth Brocard / D-triangle (CTC): K018, K539 |

first circumperp (TCCT 6.21): K100, K794 |

extangents (TCCT 6.17): K391, K750 |

Aries ETC X(5596)): K075, K191 |

anti first-Brocard (see ETC X(5939)): K699, K740 |

Yff central (TCCT 6.37): K748 |

Trinh (see ETC X(7688)): K488 |

tangential of Thomson: K172 |

tangential of excentral: K343 |

T(-2,1) (TCCT 6.41): K338 |

submedial (see ETC X(9813)): K281 |

Stammler (MathWorld): K297 |

second Neuberg (MathWorld): K422 |

second Euler (see ETC X(3758)): K044 |

outer Vecten (MathWorld): K006 |

outer inscribed squares (MathWorld): K424b |

outer Garcia (see ETC X(5587)): K033 |

outer Fermat (TCCT p178): K001 |

Lemoine (MathWorld): K283 |

Kosnita (see ETC X(1658)): K388 |

inverse in incircle: K666 |

inner Vecten (MathWorld): K006 |

inner inscribed squares (MathWorld): K424a |

inner Fermat (TCCT p178): K001 |

first orthosymmedial (see ETC X(6792)): K055 |

first Neuberg (MathWorld): K422 |

first Conway (see ETC X(7411)): K344 |

excentral of tangential: K174 |

Euler (TCCT 6.11): K026 |

complement of Stammler (see X(6070)): K741 |

circum-symmedial: K726 |

circum-medial (TCCT 6.19): K794 |

Caelum / fifth mixitilinear (see ETC X(5603)): K201 |

Ara (see ETC X(5594)): K174 |

anti fourth-Brocard (CTC): K640 |