Movatterモバイル変換

Acronym	sibrid (old: sadrid)
Name	small birhombateddodecateron, bicantellatedhexateron, equatorial cross-section ofscad-firsttrim, equatorial cross-section ofrix-firstbrox
Circumradius	sqrt(2) = 1.414214
Lace city in approx. ASCII-art	o3x3o x3x3o x3o3x -- o3x3o3x (srip) x3x3o o3u3o o3x3x -- o3x3x3o (deca) x3o3x o3x3x o3x3o-- x3o3x3o (invsrip)
Vertex figure	©
Colonel of regiment	(is itself locally convex– uniform polychoral members: by facets: deca rawvtip srip triddip rabird 6 12 0 0 sibrid 0 0 12 20 & others)
Face vector	90, 360, 420, 180, 32
Confer	relatedsegmentotera: octatuttip  sripadeca   ambification: resibrid   ambification pre-image: dot   general polytopal classes: Wythoffian polytera  lace simplices
External links

As abstract polytope sibrid is isomorphic to its (Grünbaumian)isomorph, thereby replacing some prograde by retrograde triangles,co by2thah, resp.srip bypinnip+5 2thah.

By virtue of an outer symmetry this is a non-quasiregular monotoxal polyteron, that is all edges belong to the same equivalence class.

Incidence matrix according toDynkin symbol

o3x3o3x3o. . . . . | 90 |   4   4 |  2  2   8  2  2 |  1  4  4  4  1 | 2  2 2----------+----+---------+-----------------+----------------+-------. x . . . |  2 | 180   * |  1  1   2  0  0 |  1  2  2  1  0 | 2  1 1. . . x . |  2 |   * 180 |  0  0   2  1  1 |  0  1  2  2  1 | 1  1 2----------+----+---------+-----------------+----------------+-------o3x . . . |  3 |   3   0 | 60  *   *  *  * |  1  2  0  0  0 | 2  1 0. x3o . . |  3 |   3   0 |  * 60   *  *  * |  1  0  2  0  0 | 2  0 1. x . x . |  4 |   2   2 |  *  * 180  *  * |  0  1  1  1  0 | 1  1 1. . o3x . |  3 |   0   3 |  *  *   * 60  * |  0  0  2  0  1 | 1  0 2. . . x3o |  3 |   0   3 |  *  *   *  * 60 |  0  0  0  2  1 | 0  1 2----------+----+---------+-----------------+----------------+-------o3x3o . .♦  6 |  12   0 |  4  4   0  0  0 | 15  *  *  *  * | 2  0 0o3x . x .♦  6 |   6   3 |  2  0   3  0  0 |  * 60  *  *  * | 1  1 0. x3o3x .♦ 12 |  12  12 |  0  4   6  4  0 |  *  * 30  *  * | 1  0 1. x . x3o♦  6 |   3   6 |  0  0   3  0  2 |  *  *  * 60  * | 0  1 1. . o3x3o♦  6 |   0  12 |  0  0   0  4  4 |  *  *  *  * 15 | 0  0 2----------+----+---------+-----------------+----------------+-------o3x3o3x .♦ 30 |  60  30 | 20 20  30 10  0 |  5 10  5  0  0 | 6  * *o3x . x3o♦  9 |   9   9 |  3  0   9  0  3 |  0  3  0  3  0 | * 20 *. x3o3x3o♦ 30 |  30  60 |  0 10  30 20 20 |  0  0  5 10  5 | *  * 6

or. . . . .    | 90 |   8 |   4   4   8 |  2   8  4 |  4  2-------------+----+-----+-------------+-----------+------. x . . .  & |  2 | 360 |   1   1   2 |  1   3  2 |  3  1-------------+----+-----+-------------+-----------+------o3x . . .  & |  3 |   3 | 120   *   * |  1   2  0 |  2  1. x3o . .  & |  3 |   3 |   * 120   * |  1   0  2 |  3  0. x . x .    |  4 |   4 |   *   * 180 |  0   2  1 |  2  1-------------+----+-----+-------------+-----------+------o3x3o . .  &♦  6 |  12 |   4   4   0 | 30   *  * |  2  0o3x . x .  &♦  6 |   9 |   2   0   3 |  * 120  * |  1  1. x3o3x .♦ 12 |  24 |   0   8   6 |  *   * 30 |  2  0-------------+----+-----+-------------+-----------+------o3x3o3x .  &♦ 30 |  90 |  20  30  30 |  5  10  5 | 12  *o3x . x3o♦  9 |  18 |   6   0   9 |  0   6  0 |  * 20

o3/2x3o3x3o.   . . . . | 90 |   4   4 |  2  2   8  2  2 |  1  4  4  4  1 | 2  2 2------------+----+---------+-----------------+----------------+-------.   x . . . |  2 | 180   * |  1  1   2  0  0 |  1  2  2  1  0 | 2  1 1.   . . x . |  2 |   * 180 |  0  0   2  1  1 |  0  1  2  2  1 | 1  1 2------------+----+---------+-----------------+----------------+-------o3/2x . . . |  3 |   3   0 | 60  *   *  *  * |  1  2  0  0  0 | 2  1 0.   x3o . . |  3 |   3   0 |  * 60   *  *  * |  1  0  2  0  0 | 2  0 1.   x . x . |  4 |   2   2 |  *  * 180  *  * |  0  1  1  1  0 | 1  1 1.   . o3x . |  3 |   0   3 |  *  *   * 60  * |  0  0  2  0  1 | 1  0 2.   . . x3o |  3 |   0   3 |  *  *   *  * 60 |  0  0  0  2  1 | 0  1 2------------+----+---------+-----------------+----------------+-------o3/2x3o . .♦  6 |  12   0 |  4  4   0  0  0 | 15  *  *  *  * | 2  0 0o3/2x . x .♦  6 |   6   3 |  2  0   3  0  0 |  * 60  *  *  * | 1  1 0.   x3o3x .♦ 12 |  12  12 |  0  4   6  4  0 |  *  * 30  *  * | 1  0 1.   x . x3o♦  6 |   3   6 |  0  0   3  0  2 |  *  *  * 60  * | 0  1 1.   . o3x3o♦  6 |   0  12 |  0  0   0  4  4 |  *  *  *  * 15 | 0  0 2------------+----+---------+-----------------+----------------+-------o3/2x3o3x .♦ 30 |  60  30 | 20 20  30 10  0 |  5 10  5  0  0 | 6  * *o3/2x . x3o♦  9 |   9   9 |  3  0   9  0  3 |  0  3  0  3  0 | * 20 *.   x3o3x3o♦ 30 |  30  60 |  0 10  30 20 20 |  0  0  5 10  5 | *  * 6

o3/2x3o3x3/2o.   . . .   . | 90 |   4   4 |  2  2   8  2  2 |  1  4  4  4  1 | 2  2 2--------------+----+---------+-----------------+----------------+-------.   x . .   . |  2 | 180   * |  1  1   2  0  0 |  1  2  2  1  0 | 2  1 1.   . . x   . |  2 |   * 180 |  0  0   2  1  1 |  0  1  2  2  1 | 1  1 2--------------+----+---------+-----------------+----------------+-------o3/2x . .   . |  3 |   3   0 | 60  *   *  *  * |  1  2  0  0  0 | 2  1 0.   x3o .   . |  3 |   3   0 |  * 60   *  *  * |  1  0  2  0  0 | 2  0 1.   x . x   . |  4 |   2   2 |  *  * 180  *  * |  0  1  1  1  0 | 1  1 1.   . o3x   . |  3 |   0   3 |  *  *   * 60  * |  0  0  2  0  1 | 1  0 2.   . . x3/2o |  3 |   0   3 |  *  *   *  * 60 |  0  0  0  2  1 | 0  1 2--------------+----+---------+-----------------+----------------+-------o3/2x3o .   .♦  6 |  12   0 |  4  4   0  0  0 | 15  *  *  *  * | 2  0 0o3/2x . x   .♦  6 |   6   3 |  2  0   3  0  0 |  * 60  *  *  * | 1  1 0.   x3o3x   .♦ 12 |  12  12 |  0  4   6  4  0 |  *  * 30  *  * | 1  0 1.   x . x3/2o♦  6 |   3   6 |  0  0   3  0  2 |  *  *  * 60  * | 0  1 1.   . o3x3/2o♦  6 |   0  12 |  0  0   0  4  4 |  *  *  *  * 15 | 0  0 2--------------+----+---------+-----------------+----------------+-------o3/2x3o3x   .♦ 30 |  60  30 | 20 20  30 10  0 |  5 10  5  0  0 | 6  * *o3/2x . x3/2o♦  9 |   9   9 |  3  0   9  0  3 |  0  3  0  3  0 | * 20 *.   x3o3x3/2o♦ 30 |  30  60 |  0 10  30 20 20 |  0  0  5 10  5 | *  * 6

or.   . . .   .    | 90 |   8 |   4   4   8 |  2   8  4 |  4  2-----------------+----+-----+-------------+-----------+------.   x . .   .  & |  2 | 360 |   1   1   2 |  1   3  2 |  3  1-----------------+----+-----+-------------+-----------+------o3/2x . .   .  & |  3 |   3 | 120   *   * |  1   2  0 |  2  1.   x3o .   .  & |  3 |   3 |   * 120   * |  1   0  2 |  3  0.   x . x   .    |  4 |   4 |   *   * 180 |  0   2  1 |  2  1-----------------+----+-----+-------------+-----------+------o3/2x3o .   .  &♦  6 |  12 |   4   4   0 | 30   *  * |  2  0o3/2x . x   .  &♦  6 |   9 |   2   0   3 |  * 120  * |  1  1.   x3o3x   .♦ 12 |  24 |   0   8   6 |  *   * 30 |  2  0-----------------+----+-----+-------------+-----------+------o3/2x3o3x   .  &♦ 30 |  90 |  20  30  30 |  5  10  5 | 12  *o3/2x . x3/2o♦  9 |  18 |   6   0   9 |  0   6  0 |  * 20

o3x3/2o3/2x3o. .   .   . . | 90 |   4   4 |  2  2   8  2  2 |  1  4  4  4  1 | 2  2 2--------------+----+---------+-----------------+----------------+-------. x   .   . . |  2 | 180   * |  1  1   2  0  0 |  1  2  2  1  0 | 2  1 1. .   .   x . |  2 |   * 180 |  0  0   2  1  1 |  0  1  2  2  1 | 1  1 2--------------+----+---------+-----------------+----------------+-------o3x   .   . . |  3 |   3   0 | 60  *   *  *  * |  1  2  0  0  0 | 2  1 0. x3/2o   . . |  3 |   3   0 |  * 60   *  *  * |  1  0  2  0  0 | 2  0 1. x   .   x . |  4 |   2   2 |  *  * 180  *  * |  0  1  1  1  0 | 1  1 1. .   o3/2x . |  3 |   0   3 |  *  *   * 60  * |  0  0  2  0  1 | 1  0 2. .   .   x3o |  3 |   0   3 |  *  *   *  * 60 |  0  0  0  2  1 | 0  1 2--------------+----+---------+-----------------+----------------+-------o3x3/2o   . .♦  6 |  12   0 |  4  4   0  0  0 | 15  *  *  *  * | 2  0 0o3x   .   x .♦  6 |   6   3 |  2  0   3  0  0 |  * 60  *  *  * | 1  1 0. x3/2o3/2x .♦ 12 |  12  12 |  0  4   6  4  0 |  *  * 30  *  * | 1  0 1. x   .   x3o♦  6 |   3   6 |  0  0   3  0  2 |  *  *  * 60  * | 0  1 1. .   o3/2x3o♦  6 |   0  12 |  0  0   0  4  4 |  *  *  *  * 15 | 0  0 2--------------+----+---------+-----------------+----------------+-------o3x3/2o3/2x .♦ 30 |  60  30 | 20 20  30 10  0 |  5 10  5  0  0 | 6  * *o3x   .   x3o♦  9 |   9   9 |  3  0   9  0  3 |  0  3  0  3  0 | * 20 *. x3/2o3/2x3o♦ 30 |  30  60 |  0 10  30 20 20 |  0  0  5 10  5 | *  * 6

or. .   .   . .    | 90 |   8 |   4   4   8 |  2   8  4 |  4  2-----------------+----+-----+-------------+-----------+------. x   .   . .  & |  2 | 360 |   1   1   2 |  1   3  2 |  3  1-----------------+----+-----+-------------+-----------+------o3x   .   . .  & |  3 |   3 | 120   *   * |  1   2  0 |  2  1. x3/2o   . .  & |  3 |   3 |   * 120   * |  1   0  2 |  3  0. x   .   x .    |  4 |   4 |   *   * 180 |  0   2  1 |  2  1-----------------+----+-----+-------------+-----------+------o3x3/2o   . .  &♦  6 |  12 |   4   4   0 | 30   *  * |  2  0o3x   .   x .  &♦  6 |   9 |   2   0   3 |  * 120  * |  1  1. x3/2o3/2x .♦ 12 |  24 |   0   8   6 |  *   * 30 |  2  0-----------------+----+-----+-------------+-----------+------o3x3/2o3/2x .  &♦ 30 |  90 |  20  30  30 |  5  10  5 | 12  *o3x  .   x3o♦  9 |  18 |   6   0   9 |  0   6  0 |  * 20

o3x3/2o3/2x3/2o. .   .   .   . | 90 |   4   4 |  2  2   8  2  2 |  1  4  4  4  1 | 2  2 2----------------+----+---------+-----------------+----------------+-------. x   .   .   . |  2 | 180   * |  1  1   2  0  0 |  1  2  2  1  0 | 2  1 1. .   .   x   . |  2 |   * 180 |  0  0   2  1  1 |  0  1  2  2  1 | 1  1 2----------------+----+---------+-----------------+----------------+-------o3x   .   .   . |  3 |   3   0 | 60  *   *  *  * |  1  2  0  0  0 | 2  1 0. x3/2o   .   . |  3 |   3   0 |  * 60   *  *  * |  1  0  2  0  0 | 2  0 1. x   .   x   . |  4 |   2   2 |  *  * 180  *  * |  0  1  1  1  0 | 1  1 1. .   o3/2x   . |  3 |   0   3 |  *  *   * 60  * |  0  0  2  0  1 | 1  0 2. .   .   x3/2o |  3 |   0   3 |  *  *   *  * 60 |  0  0  0  2  1 | 0  1 2----------------+----+---------+-----------------+----------------+-------o3x3/2o   .   .♦  6 |  12   0 |  4  4   0  0  0 | 15  *  *  *  * | 2  0 0o3x   .   x   .♦  6 |   6   3 |  2  0   3  0  0 |  * 60  *  *  * | 1  1 0. x3/2o3/2x   .♦ 12 |  12  12 |  0  4   6  4  0 |  *  * 30  *  * | 1  0 1. x   .   x3/2o♦  6 |   3   6 |  0  0   3  0  2 |  *  *  * 60  * | 0  1 1. .   o3/2x3/2o♦  6 |   0  12 |  0  0   0  4  4 |  *  *  *  * 15 | 0  0 2----------------+----+---------+-----------------+----------------+-------o3x3/2o3/2x   .♦ 30 |  60  30 | 20 20  30 10  0 |  5 10  5  0  0 | 6  * *o3x   .   x3/2o♦  9 |   9   9 |  3  0   9  0  3 |  0  3  0  3  0 | * 20 *. x3/2o3/2x3/2o♦ 30 |  30  60 |  0 10  30 20 20 |  0  0  5 10  5 | *  * 6

o3/2x3/2o3/2x3/2o.   .   .   .   . | 90 |   4   4 |  2  2   8  2  2 |  1  4  4  4  1 | 2  2 2------------------+----+---------+-----------------+----------------+-------.   x   .   .   . |  2 | 180   * |  1  1   2  0  0 |  1  2  2  1  0 | 2  1 1.   .   .   x   . |  2 |   * 180 |  0  0   2  1  1 |  0  1  2  2  1 | 1  1 2------------------+----+---------+-----------------+----------------+-------o3/2x   .   .   . |  3 |   3   0 | 60  *   *  *  * |  1  2  0  0  0 | 2  1 0.   x3/2o   .   . |  3 |   3   0 |  * 60   *  *  * |  1  0  2  0  0 | 2  0 1.   x   .   x   . |  4 |   2   2 |  *  * 180  *  * |  0  1  1  1  0 | 1  1 1.   .   o3/2x   . |  3 |   0   3 |  *  *   * 60  * |  0  0  2  0  1 | 1  0 2.   .   .   x3/2o |  3 |   0   3 |  *  *   *  * 60 |  0  0  0  2  1 | 0  1 2------------------+----+---------+-----------------+----------------+-------o3/2x3/2o   .   .♦  6 |  12   0 |  4  4   0  0  0 | 15  *  *  *  * | 2  0 0o3/2x   .   x   .♦  6 |   6   3 |  2  0   3  0  0 |  * 60  *  *  * | 1  1 0.   x3/2o3/2x   .♦ 12 |  12  12 |  0  4   6  4  0 |  *  * 30  *  * | 1  0 1.   x   .   x3/2o♦  6 |   3   6 |  0  0   3  0  2 |  *  *  * 60  * | 0  1 1.   .   o3/2x3/2o♦  6 |   0  12 |  0  0   0  4  4 |  *  *  *  * 15 | 0  0 2------------------+----+---------+-----------------+----------------+-------o3/2x3/2o3/2x   .♦ 30 |  60  30 | 20 20  30 10  0 |  5 10  5  0  0 | 6  * *o3/2x   .   x3/2o♦  9 |   9   9 |  3  0   9  0  3 |  0  3  0  3  0 | * 20 *.   x3/2o3/2x3/2o♦ 30 |  30  60 |  0 10  30 20 20 |  0  0  5 10  5 | *  * 6

or.   .   .   .   .    | 90 |   8 |   4   4   8 |  2   8  4 |  4  2---------------------+----+-----+-------------+-----------+------.   x   .   .   .  & |  2 | 360 |   1   1   2 |  1   3  2 |  3  1---------------------+----+-----+-------------+-----------+------o3/2x   .   .   .  & |  3 |   3 | 120   *   * |  1   2  0 |  2  1.   x3/2o   .   .  & |  3 |   3 |   * 120   * |  1   0  2 |  3  0.   x   .   x   .    |  4 |   4 |   *   * 180 |  0   2  1 |  2  1---------------------+----+-----+-------------+-----------+------o3/2x3/2o   .   .  &♦  6 |  12 |   4   4   0 | 30   *  * |  2  0o3/2x   .   x   .  &♦  6 |   9 |   2   0   3 |  * 120  * |  1  1.   x3/2o3/2x   .♦ 12 |  24 |   0   8   6 |  *   * 30 |  2  0---------------------+----+-----+-------------+-----------+------o3/2x3/2o3/2x   .  &♦ 30 |  90 |  20  30  30 |  5  10  5 | 12  *o3/2x  .   x3/2o♦  9 |  18 |   6   0   9 |  0   6  0 |  * 20

xoo3oxx3xxo3oox&#xt   → both heights = sqrt(3/5) = 0.774597(srip|| pseudodeca|| invsrip)o..3o..3o..3o..     & | 60  * |  2   4   2  0 |  1  4  2  2  2  1   4  0 |  2  2  1  1  4  2  2 | 1  3  2.o.3.o.3.o.3.o.       |  * 30 |  0   0   4  4 |  0  0  0  0  2  4   8  2 |  0  0  0  2  4  4  4 | 0  4  2----------------------+-------+---------------+--------------------------+----------------------+--------x.. ... ... ...     & |  2  0 | 60   *   *  * |  1  2  0  0  1  0   0  0 |  2  1  0  1  2  0  0 | 1  2  1... ... x.. ...     & |  2  0 |  * 120   *  * |  0  1  1  1  0  0   1  0 |  1  1  1  0  1  1  1 | 1  2  1oo.3oo.3oo.3oo.&#x  & |  1  1 |  *   * 120  * |  0  0  0  0  1  1   2  0 |  0  0  0  1  2  2  1 | 0  3  1... .x. ... ...     & |  0  2 |  *   *   * 60 |  0  0  0  0  0  1   2  1 |  0  0  0  1  1  2  2 | 0  3  1----------------------+-------+---------------+--------------------------+----------------------+--------x..3o.. ... ...     & |  3  0 |  3   0   0  0 | 20  *  *  *  *  *   *  * |  2  0  0  1  0  0  0 | 1  2  0x.. ... x.. ...     & |  4  0 |  2   2   0  0 |  * 60  *  *  *  *   *  * |  1  1  0  0  1  0  0 | 1  1  1... o..3x.. ...     & |  3  0 |  0   3   0  0 |  *  * 40  *  *  *   *  * |  1  0  1  0  0  1  0 | 1  2  0... ... x..3o..     & |  3  0 |  0   3   0  0 |  *  *  * 40  *  *   *  * |  0  1  1  0  0  0  1 | 1  1  1xo. ... ... ...&#x  & |  2  1 |  1   0   2  0 |  *  *  *  * 60  *   *  * |  0  0  0  1  2  0  0 | 0  2  1... ox. ... ...&#x  & |  1  2 |  0   0   2  1 |  *  *  *  *  * 60   *  * |  0  0  0  1  0  2  0 | 0  3  0... ... xx. ...&#x  & |  2  2 |  0   1   2  1 |  *  *  *  *  *  * 120  * |  0  0  0  0  1  1  1 | 0  2  1.o.3.x. ... ...     & |  0  3 |  0   0   0  3 |  *  *  *  *  *  *   * 20 |  0  0  0  1  0  0  2 | 0  2  1----------------------+-------+---------------+--------------------------+----------------------+--------x..3o..3x.. ...     &♦ 12  0 | 12  12   0  0 |  4  6  4  0  0  0   0  0 | 10  *  *  *  *  *  * | 1  1  0x.. ... x..3o..     &♦  6  0 |  3   6   0  0 |  0  3  0  2  0  0   0  0 |  * 20  *  *  *  *  * | 1  0  1... o..3x..3o..     &♦  6  0 |  0  12   0  0 |  0  0  4  4  0  0   0  0 |  *  * 10  *  *  *  * | 1  1  0xo.3ox. ... ...&#x  &♦  3  3 |  3   0   6  3 |  1  0  0  0  3  3   0  1 |  *  *  * 20  *  *  * | 0  2  0xo. ... xx. ...&#x  &♦  4  2 |  2   2   4  1 |  0  1  0  0  2  0   2  0 |  *  *  *  * 60  *  * | 0  1  1... oxx3xxo ...&#xt♦  6  6 |  0   6  12  6 |  0  0  2  0  0  6   6  0 |  *  *  *  *  * 20  * | 0  2  0... ... xx.3oo.&#x  &♦  3  3 |  0   3   3  3 |  0  0  0  1  0  0   3  1 |  *  *  *  *  *  * 40 | 0  1  1----------------------+-------+---------------+--------------------------+----------------------+--------x..3o..3x..3o..     &♦ 30  0 | 30  60   0  0 | 10 30 20 20  0  0   0  0 |  5 10  5  0  0  0  0 |2  *  *xoo3oxx3xxo ...&#xt &♦ 18 12 | 12  24  36 18 |  4  6  8  4 12 18  24  4 |  1  0  1  4  6  4  4 | * 10  *xo. ... xx.3oo.&#x  &♦  6  3 |  3   6   6  3 |  0  3  0  2  3  0   6  1 |  0  1  0  0  3  0  2 | *  * 20