Acronym | ... |
Name | gardatady+1440{5} |
Circumradius | sqrt[3-sqrt(5)] = 0.874032 |
General of army | hi |
Colonel of regiment | gadtaxady |
Confer |
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As abstract polytope gardatady+1440{5} is isomorphic to sirdatady+1440{5/2}, thereby interchanging pentagrams and pentagons, resp. replacing gidtid by sidtid and gid by id.
In this Grünbaumian polychoron it happens that the gidtid and the ditdid become co-realmic. Therefore any such pair looks like their blend, the sidtid, in addition to those pairs of coincident pentagons, which while blending would be reduced. Accordingly, for gardatady+1440{5}, edges and pentagons come in coincident pairs too.
Incidence matrix according to Dynkin symbol
x3o3o3o5/2*a5/4*c . . . . | 600 | 24 | 12 12 12 | 4 6 4 ------------------+-----+------+----------------+------------ x . . . | 2 | 7200 | 1 1 1 | 1 1 1 ------------------+-----+------+----------------+------------ x3o . . | 3 | 3 | 2400 * * | 1 1 0 x . o . *a5/4*c | 5 | 5 | * 1440 * | 1 0 1 x . . o5/2*a | 5 | 5 | * * 1440 | 0 1 1 ------------------+-----+------+----------------+------------ x3o3o . *a5/4*c ♦ 20 | 60 | 20 12 0 | 120 * * x3o . o5/2*a ♦ 30 | 60 | 20 0 12 | * 120 * x . o3o5/2*a5/4*c ♦ 20 | 60 | 0 12 12 | * * 120
x3o3o3/2o5/3*a5/4*c . . . . | 600 | 24 | 12 12 12 | 4 6 4 --------------------+-----+------+----------------+------------ x . . . | 2 | 7200 | 1 1 1 | 1 1 1 --------------------+-----+------+----------------+------------ x3o . . | 3 | 3 | 2400 * * | 1 1 0 x . o . *a5/4*c | 5 | 5 | * 1440 * | 1 0 1 x . . o5/3*a | 5 | 5 | * * 1440 | 0 1 1 --------------------+-----+------+----------------+------------ x3o3o . *a5/4*c ♦ 20 | 60 | 20 12 0 | 120 * * x3o . o5/3*a ♦ 30 | 60 | 20 0 12 | * 120 * x . o3/2o5/3*a5/4*c ♦ 20 | 60 | 0 12 12 | * * 120
x3o3/2o3/2o5/2*a5*c . . . . | 600 | 24 | 12 12 12 | 4 6 4 --------------------+-----+------+----------------+------------ x . . . | 2 | 7200 | 1 1 1 | 1 1 1 --------------------+-----+------+----------------+------------ x3o . . | 3 | 3 | 2400 * * | 1 1 0 x . o . *a5*c | 5 | 5 | * 1440 * | 1 0 1 x . . o5/2*a | 5 | 5 | * * 1440 | 0 1 1 --------------------+-----+------+----------------+------------ x3o3/2o . *a5*c ♦ 20 | 60 | 20 12 0 | 120 * * x3o . o5/2*a ♦ 30 | 60 | 20 0 12 | * 120 * x . o3/2o5/2*a5*c ♦ 20 | 60 | 0 12 12 | * * 120
x3o3/2o3o5/3*a5*c . . . . | 600 | 24 | 12 12 12 | 4 6 4 ------------------+-----+------+----------------+------------ x . . . | 2 | 7200 | 1 1 1 | 1 1 1 ------------------+-----+------+----------------+------------ x3o . . | 3 | 3 | 2400 * * | 1 1 0 x . o . *a5*c | 5 | 5 | * 1440 * | 1 0 1 x . . o5/3*a | 5 | 5 | * * 1440 | 0 1 1 ------------------+-----+------+----------------+------------ x3o3/2o . *a5*c ♦ 20 | 60 | 20 12 0 | 120 * * x3o . o5/3*a ♦ 30 | 60 | 20 0 12 | * 120 * x . o3o5/3*a5*c ♦ 20 | 60 | 0 12 12 | * * 120
x3/2o3o3o5/3*a5*c . . . . | 600 | 24 | 12 12 12 | 4 6 4 ------------------+-----+------+----------------+------------ x . . . | 2 | 7200 | 1 1 1 | 1 1 1 ------------------+-----+------+----------------+------------ x3/2o . . | 3 | 3 | 2400 * * | 1 1 0 x . o . *a5*c | 5 | 5 | * 1440 * | 1 0 1 x . . o5/3*a | 5 | 5 | * * 1440 | 0 1 1 ------------------+-----+------+----------------+------------ x3/2o3o . *a5*c ♦ 20 | 60 | 20 12 0 | 120 * * x3/2o . o5/3*a ♦ 30 | 60 | 20 0 12 | * 120 * x . o3o5/3*a5*c ♦ 20 | 60 | 0 12 12 | * * 120
x3/2o3o3/2o5/2*a5*c . . . . | 600 | 24 | 12 12 12 | 4 6 4 --------------------+-----+------+----------------+------------ x . . . | 2 | 7200 | 1 1 1 | 1 1 1 --------------------+-----+------+----------------+------------ x3/2o . . | 3 | 3 | 2400 * * | 1 1 0 x . o . *a5*c | 5 | 5 | * 1440 * | 1 0 1 x . . o5/2*a | 5 | 5 | * * 1440 | 0 1 1 --------------------+-----+------+----------------+------------ x3/2o3o . *a5*c ♦ 20 | 60 | 20 12 0 | 120 * * x3/2o . o5/2*a ♦ 30 | 60 | 20 0 12 | * 120 * x . o3/2o5/2*a5*c ♦ 20 | 60 | 0 12 12 | * * 120
x3/2o3/2o3o5/2*a5/4*c . . . . | 600 | 24 | 12 12 12 | 4 6 4 ----------------------+-----+------+----------------+------------ x . . . | 2 | 7200 | 1 1 1 | 1 1 1 ----------------------+-----+------+----------------+------------ x3/2o . . | 3 | 3 | 2400 * * | 1 1 0 x . o . *a5/4*c | 5 | 5 | * 1440 * | 1 0 1 x . . o5/2*a | 5 | 5 | * * 1440 | 0 1 1 ----------------------+-----+------+----------------+------------ x3/2o3/2o . *a5/4*c ♦ 20 | 60 | 20 12 0 | 120 * * x3/2o . o5/2*a ♦ 30 | 60 | 20 0 12 | * 120 * x . o3o5/2*a5/4*c ♦ 20 | 60 | 0 12 12 | * * 120
x3/2o3/2o3/2o5/3*a5/4*c . . . . | 600 | 24 | 12 12 12 | 4 6 4 ------------------------+-----+------+----------------+------------ x . . . | 2 | 7200 | 1 1 1 | 1 1 1 ------------------------+-----+------+----------------+------------ x3/2o . . | 3 | 3 | 2400 * * | 1 1 0 x . o . *a5/4*c | 5 | 5 | * 1440 * | 1 0 1 x . . o5/3*a | 5 | 5 | * * 1440 | 0 1 1 ------------------------+-----+------+----------------+------------ x3/2o3/2o . *a5/4*c ♦ 20 | 60 | 20 12 0 | 120 * * x3/2o . o5/3*a ♦ 30 | 60 | 20 0 12 | * 120 * x . o3/2o5/3*a5/4*c ♦ 20 | 60 | 0 12 12 | * * 120
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