Acronym dotu
Name dot-based ursapeton
Circumradius sqrt[(25+9 sqrt(5))/22] = 1.432173
Face vector 130, 650, 990, 660, 224, 34
Confer
general polytopal classes:
ursatopes  

Incidence matrix according to Dynkin symbol

ooo3xoo3ofx3xoo3ooo&#xt   → height(1,2) = sqrt[(5 sqrt(5)-9)/8] = 0.522056
                            height(2,3) = sqrt[(3 sqrt(5)-1)/8] = 0.844704
(sibrid || f-dot || dot)

o..3o..3o..3o..3o..       | 90  *  * |   8   2  0  0 |   4   4   8   8  1   0 |  2   8  4   4   4   8  0  0 |  4  2  2   8  4  0 | 1  4  2 0
.o.3.o.3.o.3.o.3.o.       |  * 20  * |   0   9  1  0 |   0   0   0  18  9   0 |  0   0  0   6  18   9  0  0 |  0  0  6   6  9  0 | 0  6  1 0
..o3..o3..o3..o3..o       |  *  * 20 |   0   0  1  9 |   0   0   0   0  9  18 |  0   0  0   0  18   0  6  9 |  0  0  6   0  9  6 | 0  6  0 1
--------------------------+----------+---------------+------------------------+-----------------------------+--------------------+----------
... x.. ... ... ...     & |  2  0  0 | 360   *  *  * |   1   1   2   1  0   0 |  1   3  2   1   1   2  0  0 |  3  1  1   3  2  0 | 1  3  1 0
oo.3oo.3oo.3oo.3oo.&#x    |  1  1  0 |   * 180  *  * |   0   0   0   4  1   0 |  0   0  0   2   4   4  0  0 |  0  0  2   4  4  0 | 0  4  1 0
.oo3.oo3.oo3.oo3.oo&#x    |  0  1  1 |   *   * 20  *    0   0   0   0  9   0 |  0   0  0   0  18   0  0  0 |  0  0  6   0  9  0 | 0  6  0 0
... ... ..x ... ...       |  0  0  2 |   *   *  * 90 |   0   0   0   0  1   4 |  0   0  0   0   4   0  2  4 |  0  0  2   0  4  4 | 0  4  0 1
--------------------------+----------+---------------+------------------------+-----------------------------+--------------------+----------
o..3x.. ... ... ...     & |  3  0  0 |   3   0  0  0 | 120   *   *   *  *   * |  1   2  0   1   0   0  0  0 |  2  1  1   2  0  0 | 1  2  1 0
... x..3o.. ... ...     & |  3  0  0 |   3   0  0  0 |   * 120   *   *  *   * |  1   0  2   0   1   0  0  0 |  3  0  1   0  2  0 | 1  3  0 0
... x.. ... x.. ...       |  4  0  0 |   4   0  0  0 |   *   * 180   *  *   * |  0   2  1   0   0   1  0  0 |  2  1  0   2  1  0 | 1  2  1 0
... xo. ... ... ...&#x  & |  2  1  0 |   1   2  0  0 |   *   *   * 360  *   * |  0   0  0   1   1   2  0  0 |  0  0  1   3  2  0 | 0  3  1 0
... ... ofx ... ...&#xt   |  1  2  2 |   0   2  2  1 |   *   *   *   * 90   * |  0   0  0   0   4   0  0  0 |  0  0  2   0  4  0 | 0  4  0 0
... ..o3..x ... ...     & |  0  0  3 |   0   0  0  3 |   *   *   *   *  * 120 |  0   0  0   0   1   0  1  2 |  0  0  1   0  2  3 | 0  3  0 1
--------------------------+----------+---------------+------------------------+-----------------------------+--------------------+----------
o..3x..3o.. ... ...     &   6  0  0 |  12   0  0  0 |   4   4   0   0  0   0 | 30   *  *   *   *   *  *  * |  2  0  1   0  0  0 | 1  2  0 0
o..3x.. ... x.. ...     &   6  0  0 |   9   0  0  0 |   2   0   3   0  0   0 |  * 120  *   *   *   *  *  * |  1  1  0   1  0  0 | 1  1  1 0
... x..3o..3x.. ...        12  0  0 |  24   0  0  0 |   0   8   6   0  0   0 |  *   * 30   *   *   *  *  * |  2  0  0   0  1  0 | 1  2  0 0
oo.3xo. ... ... ...&#x  &   3  1  0 |   3   3  0  0 |   1   0   0   3  0   0 |  *   *  * 120   *   *  *  * |  0  0  1   2  0  0 | 0  2  1 0
... xoo3ofx ... ...&#xt &   3  3  3 |   3   6  3  3 |   0   1   0   3  3   1 |  *   *  *   * 120   *  *  * |  0  0  1   0  2  0 | 0  3  0 0
... xo. ... xo. ...&#x      4  1  0 |   4   4  0  0 |   0   0   1   4  0   0 |  *   *  *   *   * 180  *  * |  0  0  0   2  1  0 | 0  2  1 0
..o3..o3..x ... ...     &   0  0  4 |   0   0  0  6 |   0   0   0   0  0   4 |  *   *  *   *   *   * 30  * |  0  0  1   0  0  2 | 0  2  0 1
... ..o3..x3..o ...         0  0  6 |   0   0  0 12 |   0   0   0   0  0   8 |  *   *  *   *   *   *  * 30 |  0  0  0   0  1  2 | 0  2  0 1
--------------------------+----------+---------------+------------------------+-----------------------------+--------------------+----------
o..3x..3o..3x.. ...     &  30  0  0 |  90   0  0  0 |  20  30  30   0  0   0 |  5  10  5   0   0   0  0  0 | 12  *  *   *  *  * | 1  1  0 0
o..3x.. ... x..3o..         9  0  0 |  18   0  0  0 |   6   0   9   0  0   0 |  0   6  0   0   0   0  0  0 |  * 20  *   *  *  * | 1  0  1 0
ooo3xoo3ofx ... ...&#xt &   6  4  4 |  12  12  4  6 |   4   4   0  12  6   4 |  1   0  0   4   4   0  1  0 |  *  * 30   *  *  * | 0  2  0 0
oo.3xo. ... xo. ...&#x  &   6  1  0 |   9   6  0  0 |   2   0   3   9  0   0 |  0   1  0   2   0   3  0  0 |  *  *  * 120  *  * | 0  1  1 0
... xoo3ofx3xoo ...&#xt    12  6  6 |  24  24  6 12 |   0   8   6  24 12   8 |  0   0  1   0   8   6  0  1 |  *  *  *   * 30  * | 0  2  0 0
..o3..o3..x3..o ...     &   0  0 10 |   0   0  0 30 |   0   0   0   0  0  30 |  0   0  0   0   0   0  5  5 |  *  *  *   *  * 12 | 0  1  0 1
--------------------------+----------+---------------+------------------------+-----------------------------+--------------------+----------
o..3x..3o..3x..3o..        90  0  0 | 360   0  0  0 | 120 120 180   0  0   0 | 30 120 30   0   0   0  0  0 | 12 20  0   0  0  0 | 1  *  * *
ooo3xoo3ofx3xoo ...&#xt &  30 10 10 |  90  60 10 30 |  20  30  30  90 30  30 |  5  10  5  20  30  30  5  5 |  1  0  5  10  5  1 | * 12  * *
oo.3xo. ... xo.3oo.&#x      9  1  0 |  18   9  0  0 |   6   0   9  18  0   0 |  0   6  0   6   0   9  0  0 |  0  1  0   6  0  0 | *  * 20 *
..o3..o3..x3..o3..o         0  0 20 |   0   0  0 90 |   0   0   0   0  0 120 |  0   0  0   0   0   0 30 30 |  0  0  0   0  0 12 | *  *  * 1

© 2004-2024
top of page