- more general:
- n,co-dip
- segmentotera:
- hatricu
- general polytopal classes:
- Wythoffian polytera segmentotera lace simplices
links
| Acronym | haco (old: hicco) |
| Name | hexagon cuboctahedron duoprism |
| Circumradius | sqrt(2) = 1.414214 |
| Volume | 5 sqrt(6)/2 = 6.123724 |
| Face vector | 72, 216, 240, 114, 20 |
| Confer |
|
|
External links |
|
Incidence matrix according to Dynkin symbol
x6o o3x4o . . . . . | 72 | 2 4 | 1 8 2 2 | 4 4 4 1 | 2 2 2 ----------+----+--------+--------------+------------+------ x . . . . | 2 | 72 * | 1 4 0 0 | 4 2 2 0 | 2 2 1 . . . x . | 2 | * 144 | 0 2 1 1 | 1 2 2 1 | 1 1 2 ----------+----+--------+--------------+------------+------ x6o . . . | 6 | 6 0 | 12 * * * | 4 0 0 0 | 2 2 0 x . . x . | 4 | 2 2 | * 144 * * | 1 1 1 0 | 1 1 1 . . o3x . | 3 | 0 3 | * * 48 * | 0 2 0 1 | 1 0 2 . . . x4o | 4 | 0 4 | * * * 36 | 0 0 2 1 | 0 1 2 ----------+----+--------+--------------+------------+------ x6o . x . ♦ 12 | 12 6 | 2 6 0 0 | 24 * * * | 1 1 0 x . o3x . ♦ 6 | 3 6 | 0 3 2 0 | * 48 * * | 1 0 1 x . . x4o ♦ 8 | 4 8 | 0 4 0 2 | * * 36 * | 0 1 1 . . o3x4o ♦ 12 | 0 24 | 0 0 8 6 | * * * 6 | 0 0 2 ----------+----+--------+--------------+------------+------ x6o o3x . ♦ 18 | 18 18 | 3 18 6 0 | 3 6 0 0 | 8 * * x6o . x4o ♦ 24 | 24 24 | 4 24 0 6 | 4 0 6 0 | * 6 * x . o3x4o ♦ 24 | 12 48 | 0 24 16 12 | 0 8 6 2 | * * 6
x3x o3x4o . . . . . | 72 | 1 1 4 | 1 4 4 2 2 | 4 2 2 2 2 1 | 2 2 1 1 ----------+----+-----------+----------------+------------------+-------- x . . . . | 2 | 36 * * | 1 4 0 0 0 | 4 2 2 0 0 0 | 2 2 1 0 . x . . . | 2 | * 36 * | 1 0 4 0 0 | 4 0 0 2 2 0 | 2 2 0 1 . . . x . | 2 | * * 144 | 0 1 1 1 1 | 1 1 1 1 1 1 | 1 1 1 1 ----------+----+-----------+----------------+------------------+-------- x3x . . . | 6 | 3 3 0 | 12 * * * * | 4 0 0 0 0 0 | 2 2 0 0 x . . x . | 4 | 2 0 2 | * 72 * * * | 1 1 1 0 0 0 | 1 1 1 0 . x . x . | 4 | 0 2 2 | * * 72 * * | 1 0 0 1 1 0 | 1 1 0 1 . . o3x . | 3 | 0 0 3 | * * * 48 * | 0 1 0 1 0 1 | 1 0 1 1 . . . x4o | 4 | 0 0 4 | * * * * 36 | 0 0 1 0 1 1 | 0 1 1 1 ----------+----+-----------+----------------+------------------+-------- x3x . x . ♦ 12 | 6 6 6 | 2 3 3 0 0 | 24 * * * * * | 1 1 0 0 x . o3x . ♦ 6 | 3 0 6 | 0 3 0 2 0 | * 24 * * * * | 1 0 1 0 x . . x4o ♦ 8 | 4 0 8 | 0 4 0 0 2 | * * 18 * * * | 0 1 1 0 . x o3x . ♦ 6 | 0 3 6 | 0 0 3 2 0 | * * * 24 * * | 1 0 0 1 . x . x4o ♦ 8 | 0 4 8 | 0 0 4 0 2 | * * * * 18 * | 0 1 0 1 . . o3x4o ♦ 12 | 0 0 24 | 0 0 0 8 6 | * * * * * 6 | 0 0 1 1 ----------+----+-----------+----------------+------------------+-------- x3x o3x . ♦ 18 | 9 9 18 | 3 9 9 6 0 | 3 3 0 3 0 0 | 8 * * * x3x . x4o ♦ 24 | 12 12 24 | 4 12 12 0 6 | 4 0 3 0 3 0 | * 6 * * x . o3x4o ♦ 24 | 12 0 48 | 0 24 0 16 12 | 0 8 6 0 0 2 | * * 3 * . x o3x4o ♦ 24 | 0 12 48 | 0 0 24 16 12 | 0 0 0 8 6 2 | * * * 3
x6o x3o3x . . . . . | 72 | 2 2 2 | 1 4 4 1 2 1 | 2 2 2 4 2 1 | 1 2 1 2 ----------+----+----------+-------------------+------------------+-------- x . . . . | 2 | 72 * * | 1 2 2 0 0 0 | 2 2 1 2 1 0 | 1 2 1 1 . . x . . | 2 | * 72 * | 0 2 0 1 1 0 | 1 0 2 2 0 1 | 1 1 0 2 . . . . x | 2 | * * 72 | 0 0 2 0 1 1 | 0 1 0 2 2 1 | 0 1 1 2 ----------+----+----------+-------------------+------------------+-------- x6o . . . | 6 | 6 0 0 | 12 * * * * * | 2 2 0 0 0 0 | 1 2 1 0 x . x . . | 4 | 2 2 0 | * 72 * * * * | 1 0 1 1 0 0 | 1 1 0 1 x . . . x | 4 | 2 0 2 | * * 72 * * * | 0 1 0 1 1 0 | 0 1 1 1 . . x3o . | 3 | 0 3 0 | * * * 24 * * | 0 0 2 0 0 1 | 1 0 0 2 . . x . x | 4 | 0 2 2 | * * * * 36 * | 0 0 0 2 0 1 | 0 1 0 2 . . . o3x | 3 | 0 0 3 | * * * * * 24 | 0 0 0 0 2 1 | 0 0 1 2 ----------+----+----------+-------------------+------------------+-------- x6o x . . ♦ 12 | 12 6 0 | 2 6 0 0 0 0 | 12 * * * * * | 1 1 0 0 x6o . . x ♦ 12 | 12 0 6 | 2 0 6 0 0 0 | * 12 * * * * | 0 1 1 0 x . x3o . ♦ 6 | 3 6 0 | 0 3 0 2 0 0 | * * 24 * * * | 1 0 0 1 x . x . x ♦ 8 | 4 4 4 | 0 2 2 0 2 0 | * * * 36 * * | 0 1 0 1 x . . o3x ♦ 6 | 3 0 6 | 0 0 3 0 0 2 | * * * * 24 * | 0 0 1 1 . . x3o3x ♦ 12 | 0 12 12 | 0 0 0 4 6 4 | * * * * * 6 | 0 0 0 2 ----------+----+----------+-------------------+------------------+-------- x6o x3o . ♦ 18 | 18 18 0 | 3 18 0 6 0 0 | 3 0 6 0 0 0 | 4 * * * x6o x . x ♦ 24 | 24 12 12 | 4 12 12 0 6 0 | 2 2 0 6 0 0 | * 6 * * x6o . o3x ♦ 18 | 18 0 18 | 3 0 18 0 0 6 | 0 3 0 0 6 0 | * * 4 * x . x3o3x ♦ 24 | 12 24 24 | 0 12 12 8 12 8 | 0 0 4 6 4 2 | * * * 6
x3x x3o3x . . . . . | 72 | 1 1 2 2 | 1 2 2 2 2 1 2 1 | 2 2 1 2 1 1 2 1 1 | 1 2 1 1 1 ----------+----+-------------+-------------------------+---------------------------+---------- x . . . . | 2 | 36 * * * | 1 2 2 0 0 0 0 0 | 2 2 1 2 1 0 0 0 0 | 1 2 1 1 0 . x . . . | 2 | * 36 * * | 1 0 0 2 2 0 0 0 | 2 2 0 0 0 1 2 1 0 | 1 2 1 0 1 . . x . . | 2 | * * 72 * | 0 1 0 1 0 1 1 0 | 1 0 1 1 0 1 1 0 1 | 1 1 0 1 1 . . . . x | 2 | * * * 72 | 0 0 1 0 1 0 1 1 | 0 1 0 1 1 0 1 1 1 | 0 1 1 1 1 ----------+----+-------------+-------------------------+---------------------------+---------- x3x . . . | 6 | 3 3 0 0 | 12 * * * * * * * | 2 2 0 0 0 0 0 0 0 | 1 2 1 0 0 x . x . . | 4 | 2 0 2 0 | * 36 * * * * * * | 1 0 1 1 0 0 0 0 0 | 1 1 0 1 0 x . . . x | 4 | 2 0 0 2 | * * 36 * * * * * | 0 1 0 1 1 0 0 0 0 | 0 1 1 1 0 . x x . . | 4 | 0 2 2 0 | * * * 36 * * * * | 1 0 0 0 0 1 1 0 0 | 1 1 0 0 1 . x . . x | 4 | 0 2 0 2 | * * * * 36 * * * | 0 1 0 0 0 0 1 1 0 | 0 1 1 0 1 . . x3o . | 3 | 0 0 3 0 | * * * * * 24 * * | 0 0 1 0 0 1 0 0 1 | 1 0 0 1 1 . . x . x | 4 | 0 0 2 2 | * * * * * * 36 * | 0 0 0 1 0 0 1 0 1 | 0 1 0 1 1 . . . o3x | 3 | 0 0 0 3 | * * * * * * * 24 | 0 0 0 0 1 0 0 1 1 | 0 0 1 1 1 ----------+----+-------------+-------------------------+---------------------------+---------- x3x x . . ♦ 12 | 6 6 6 0 | 2 3 0 3 0 0 0 0 | 12 * * * * * * * * | 1 1 0 0 0 x3x . . x ♦ 12 | 6 6 0 6 | 2 0 3 0 3 0 0 0 | * 12 * * * * * * * | 0 1 1 0 0 x . x3o . ♦ 6 | 3 0 6 0 | 0 3 0 0 0 2 0 0 | * * 12 * * * * * * | 1 0 0 1 0 x . x . x ♦ 8 | 4 0 4 4 | 0 2 2 0 0 0 2 0 | * * * 18 * * * * * | 0 1 0 1 0 x . . o3x ♦ 6 | 3 0 0 6 | 0 0 3 0 0 0 0 2 | * * * * 12 * * * * | 0 0 1 1 0 . x x3o . ♦ 6 | 0 3 6 0 | 0 0 0 3 0 2 0 0 | * * * * * 12 * * * | 1 0 0 0 1 . x x . x ♦ 8 | 0 4 4 4 | 0 0 0 2 2 0 2 0 | * * * * * * 18 * * | 0 1 0 0 1 . x . o3x ♦ 6 | 0 3 0 6 | 0 0 0 0 3 0 0 2 | * * * * * * * 12 * | 0 0 1 0 1 . . x3o3x ♦ 12 | 0 0 12 12 | 0 0 0 0 0 4 6 4 | * * * * * * * * 6 | 0 0 0 1 1 ----------+----+-------------+-------------------------+---------------------------+---------- x3x x3o . ♦ 18 | 9 9 18 0 | 3 9 0 9 0 6 0 0 | 3 0 3 0 0 3 0 0 0 | 4 * * * * x3x x . x ♦ 24 | 12 12 12 12 | 4 6 6 6 6 0 6 0 | 2 2 0 3 0 0 3 0 0 | * 6 * * * x3x . o3x ♦ 18 | 9 9 0 18 | 3 0 9 0 9 0 0 6 | 0 3 0 0 3 0 0 3 0 | * * 4 * * x . x3o3x ♦ 24 | 12 0 24 24 | 0 12 12 0 0 8 12 8 | 0 0 4 6 4 0 0 0 2 | * * * 3 * . x x3o3x ♦ 24 | 0 12 24 24 | 0 0 0 12 12 8 12 8 | 0 0 0 0 0 4 6 4 2 | * * * * 3
oxx3xxo xxx3xxx&#xt → both heights = sqrt(2/3) = 0.816497 (thiddip || pseudo hiddip || gyro thiddip) o..3o.. o..3o.. & | 36 * | 2 1 1 2 0 0 0 | 1 2 2 1 1 2 2 2 0 0 0 | 1 1 2 1 1 1 2 2 2 0 | 1 1 1 1 2 .o.3.o. .o.3.o. | * 36 | 0 0 0 2 2 1 1 | 0 0 0 0 2 2 2 2 2 2 1 | 0 0 0 1 2 2 2 2 2 2 | 0 1 1 2 2 ----------------------+-------+----------------------+--------------------------------+--------------------------+---------- ... x.. ... ... & | 2 0 | 36 * * * * * * | 1 1 1 0 0 1 0 0 0 0 0 | 1 1 1 1 0 0 1 1 0 0 | 1 1 1 0 1 ... ... x.. ... & | 2 0 | * 18 * * * * * | 0 2 0 1 0 0 2 0 0 0 0 | 1 0 2 0 1 0 2 0 2 0 | 1 1 0 1 2 ... ... ... x.. & | 2 0 | * * 18 * * * * | 0 0 2 1 0 0 0 2 0 0 0 | 0 1 2 0 0 1 0 2 2 0 | 1 0 1 1 2 oo.3oo. oo.3oo.&#x & | 1 1 | * * * 72 * * * | 0 0 0 0 1 1 1 1 0 0 0 | 0 0 0 1 1 1 1 1 1 0 | 0 1 1 1 1 .x. ... ... ... & | 0 2 | * * * * 36 * * | 0 0 0 0 1 1 0 0 1 1 0 | 0 0 0 1 1 1 1 1 0 1 | 0 1 1 1 1 ... ... .x. ... & | 0 2 | * * * * * 18 * | 0 0 0 0 0 0 2 0 2 0 1 | 0 0 0 0 2 0 2 0 2 2 | 0 1 0 2 2 ... ... ... .x. & | 0 2 | * * * * * * 18 | 0 0 0 0 0 0 0 2 0 2 1 | 0 0 0 0 0 2 0 2 2 2 | 0 0 1 2 2 ----------------------+-------+----------------------+--------------------------------+--------------------------+---------- o..3x.. ... ... & | 3 0 | 3 0 0 0 0 0 0 | 12 * * * * * * * * * * | 1 1 0 1 0 0 0 0 0 0 | 1 1 1 0 0 ... x.. x.. ... & | 4 0 | 2 2 0 0 0 0 0 | * 18 * * * * * * * * * | 1 0 1 0 0 0 1 0 0 0 | 1 1 0 0 1 ... x.. ... x.. & | 4 0 | 2 0 2 0 0 0 0 | * * 18 * * * * * * * * | 0 1 1 0 0 0 0 1 0 0 | 1 0 1 0 1 ... ... x..3x.. & | 6 0 | 0 3 3 0 0 0 0 | * * * 6 * * * * * * * | 0 0 2 0 0 0 0 0 2 0 | 1 0 0 1 2 ox. ... ... ...&#x & | 1 2 | 0 0 0 2 1 0 0 | * * * * 36 * * * * * * | 0 0 0 1 1 1 0 0 0 0 | 0 1 1 1 0 ... xx. ... ...&#x & | 2 2 | 1 0 0 2 1 0 0 | * * * * * 36 * * * * * | 0 0 0 1 0 0 1 1 0 0 | 0 1 1 0 1 ... ... xx. ...&#x & | 2 2 | 0 1 0 2 0 1 0 | * * * * * * 36 * * * * | 0 0 0 0 1 0 1 0 1 0 | 0 1 0 1 1 ... ... ... xx.&#x & | 2 2 | 0 0 1 2 0 0 1 | * * * * * * * 36 * * * | 0 0 0 0 0 1 0 1 1 0 | 0 0 1 1 1 .x. ... .x. ... & | 0 4 | 0 0 0 0 2 2 0 | * * * * * * * * 18 * * | 0 0 0 0 1 0 1 0 0 1 | 0 1 0 1 1 .x. ... ... .x. & | 0 4 | 0 0 0 0 2 0 2 | * * * * * * * * * 18 * | 0 0 0 0 0 1 0 1 0 1 | 0 0 1 1 1 ... ... .x.3.x. | 0 6 | 0 0 0 0 0 3 3 | * * * * * * * * * * 6 | 0 0 0 0 0 0 0 0 2 2 | 0 0 0 2 2 ----------------------+-------+----------------------+--------------------------------+--------------------------+---------- o..3x.. x.. ... & ♦ 6 0 | 6 3 0 0 0 0 0 | 2 3 0 0 0 0 0 0 0 0 0 | 6 * * * * * * * * * | 1 1 0 0 0 o..3x.. ... x.. & ♦ 6 0 | 6 0 3 0 0 0 0 | 2 0 3 0 0 0 0 0 0 0 0 | * 6 * * * * * * * * | 1 0 1 0 0 ... x.. x..3x.. & ♦ 12 0 | 6 6 6 0 0 0 0 | 0 3 3 2 0 0 0 0 0 0 0 | * * 6 * * * * * * * | 1 0 0 0 1 oxx3xxo ... ...&#xt ♦ 6 6 | 6 0 0 12 6 0 0 | 2 0 0 0 6 6 0 0 0 0 0 | * * * 6 * * * * * * | 0 1 1 0 0 ox. ... xx. ...&#x & ♦ 2 4 | 0 1 0 4 2 2 0 | 0 0 0 0 2 0 2 0 1 0 0 | * * * * 18 * * * * * | 0 1 0 1 0 ox. ... ... xx.&#x & ♦ 2 4 | 0 0 1 4 2 0 2 | 0 0 0 0 2 0 0 2 0 1 0 | * * * * * 18 * * * * | 0 0 1 1 0 ... xx. xx. ...&#x & ♦ 4 4 | 2 2 0 4 2 2 0 | 0 1 0 0 0 2 2 0 1 0 0 | * * * * * * 18 * * * | 0 1 0 0 1 ... xx. ... xx.&#x & ♦ 4 4 | 2 0 2 4 2 0 2 | 0 0 1 0 0 2 0 2 0 1 0 | * * * * * * * 18 * * | 0 0 1 0 1 ... ... xx.3xx.&#x & ♦ 6 6 | 0 3 3 6 0 3 3 | 0 0 0 1 0 0 3 3 0 0 1 | * * * * * * * * 12 * | 0 0 0 1 1 .x. ... .x.3.x. & ♦ 0 12 | 0 0 0 0 6 6 6 | 0 0 0 0 0 0 0 0 3 3 2 | * * * * * * * * * 6 | 0 0 0 1 1 ----------------------+-------+----------------------+--------------------------------+--------------------------+---------- o..3x.. x..3x.. & ♦ 18 0 | 18 9 9 0 0 0 0 | 6 9 9 3 0 0 0 0 0 0 0 | 3 3 3 0 0 0 0 0 0 0 | 2 * * * * oxx3xxo xxx ...&#xt ♦ 12 12 | 12 6 0 24 12 6 0 | 4 6 0 0 12 12 12 0 6 0 0 | 2 0 0 2 6 0 6 0 0 0 | * 3 * * * oxx3xxo ... xxx&#xt ♦ 12 12 | 12 0 6 24 12 0 6 | 4 0 6 0 12 12 0 12 0 6 0 | 0 2 0 2 0 6 0 6 0 0 | * * 3 * * ox. ... xx.3xx.&#x & ♦ 6 12 | 0 3 3 12 6 6 6 | 0 0 0 1 6 0 6 6 3 3 2 | 0 0 0 0 3 3 0 0 2 1 | * * * 6 * ... xx. xx.3xx.&#x & ♦ 12 12 | 6 6 6 12 6 6 6 | 0 3 3 2 0 6 6 6 3 3 2 | 0 0 1 0 0 0 3 3 2 1 | * * * * 6
© 2004-2024 | top of page |