vertex figure of ranq
(at margins)
- related segmentopeta:
- tetafip
- general polytopal classes:
- Wythoffian polypeta segmentopeta lace simplices
links
| Acronym | hinnip |
| Name |
hemipenteractic prism, vertex figure of ranq |
| Circumradius | sqrt(7/8) = 0.935414 |
| Coordinates | (1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/2) & all even changes of sign in all but last coord., change of sign in last coord. |
| Volume | 13 sqrt(2)/120 = 0.153206 |
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Dihedral angles
(at margins) | |
| Face vector | 32, 176, 400, 400, 172, 28 |
| Confer |
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External links |
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Incidence matrix according to Dynkin symbol
x x3o3o *c3o3o . . . . . . | 32 | 1 10 | 10 30 | 30 10 20 | 10 20 5 5 | 5 5 1 ---------------+----+--------+--------+------------+-------------+-------- x . . . . . | 2 | 16 * ♦ 10 0 | 30 0 0 | 10 20 0 0 | 5 5 0 . x . . . . | 2 | * 160 | 1 6 | 6 3 6 | 3 6 3 2 | 3 2 1 ---------------+----+--------+--------+------------+-------------+-------- x x . . . . | 4 | 2 2 | 80 * ♦ 6 0 0 | 3 6 0 0 | 3 2 0 . x3o . . . | 3 | 0 3 | * 320 | 1 1 2 | 1 2 2 1 | 2 1 1 ---------------+----+--------+--------+------------+-------------+-------- x x3o . . . ♦ 6 | 3 6 | 3 2 | 160 * * | 1 2 0 0 | 2 1 0 . x3o3o . . ♦ 4 | 0 6 | 0 4 | * 80 * | 1 0 2 0 | 2 0 1 . x3o . *c3o . ♦ 4 | 0 6 | 0 4 | * * 160 | 0 1 1 1 | 1 1 1 ---------------+----+--------+--------+------------+-------------+-------- x x3o3o . . ♦ 8 | 4 12 | 6 8 | 4 2 0 | 40 * * * | 2 0 0 x x3o . *c3o . ♦ 8 | 4 12 | 6 8 | 4 0 2 | * 80 * * | 1 1 0 . x3o3o *c3o . ♦ 8 | 0 24 | 0 32 | 0 8 8 | * * 20 * | 1 0 1 . x3o . *c3o3o ♦ 5 | 0 10 | 0 10 | 0 0 5 | * * * 32 | 0 1 1 ---------------+----+--------+--------+------------+-------------+-------- x x3o3o *c3o . ♦ 16 | 8 48 | 24 64 | 32 16 16 | 8 8 2 0 | 10 * * x x3o . *c3o3o ♦ 10 | 5 20 | 10 20 | 10 0 10 | 0 5 0 2 | * 16 * . x3o3o *c3o3o ♦ 16 | 0 80 | 0 160 | 0 40 80 | 0 0 10 16 | * * 2
xx3oo3oo *b3oo3oo&#x → height = 1 o.3o.3o. *b3o.3o. | 16 * | 10 1 0 | 30 10 0 | 10 20 30 0 0 | 5 5 10 20 0 0 | 1 5 5 0 .o3.o3.o *b3.o3.o | * 16 | 0 1 10 | 0 10 30 | 0 0 30 10 20 | 0 0 10 20 5 5 | 0 5 5 1 ---------------------+-------+----------+------------+-----------------+-------------------+---------- x. .. .. .. .. | 2 0 | 80 * * | 6 1 0 | 3 6 6 0 0 | 3 2 3 6 0 0 | 1 3 2 0 oo3oo3oo *b3oo3oo&#x | 1 1 | * 16 * ♦ 0 10 0 | 0 0 30 0 0 | 0 0 10 20 0 0 | 0 5 5 0 .x .. .. .. .. | 0 2 | * * 80 | 0 1 6 | 0 0 6 3 6 | 0 0 3 6 3 2 | 0 3 2 1 ---------------------+-------+----------+------------+-----------------+-------------------+---------- x.3o. .. .. .. | 3 0 | 3 0 0 | 160 * * | 1 2 1 0 0 | 2 1 1 2 0 0 | 1 2 1 0 xx .. .. .. ..&#x | 2 2 | 1 2 1 | * 80 * ♦ 0 0 6 0 0 | 0 0 3 6 0 0 | 0 3 2 0 .x3.o .. .. .. | 0 3 | 0 0 3 | * * 160 | 0 0 1 1 2 | 0 0 1 2 2 1 | 0 2 1 1 ---------------------+-------+----------+------------+-----------------+-------------------+---------- x.3o.3o. .. .. ♦ 4 0 | 6 0 0 | 4 0 0 | 40 * * * * | 2 0 1 0 0 0 | 1 2 0 0 x.3o. .. *b3o. .. ♦ 4 0 | 6 0 0 | 4 0 0 | * 80 * * * | 1 1 0 1 0 0 | 1 1 1 0 xx3oo .. .. ..&#x ♦ 3 3 | 3 3 3 | 1 3 1 | * * 160 * * | 0 0 1 2 0 0 | 0 2 1 0 .x3.o3.o .. .. ♦ 0 4 | 0 0 6 | 0 0 4 | * * * 40 * | 0 0 1 0 2 0 | 0 2 0 1 .x3.o .. *b3.o .. ♦ 0 4 | 0 0 6 | 0 0 4 | * * * * 80 | 0 0 0 1 1 1 | 0 1 1 1 ---------------------+-------+----------+------------+-----------------+-------------------+---------- x.3o.3o. *b3o. .. ♦ 8 0 | 24 0 0 | 32 0 0 | 8 8 0 0 0 | 10 * * * * * | 1 1 0 0 x.3o. .. *b3o.3o. ♦ 5 0 | 10 0 0 | 10 0 0 | 0 5 0 0 0 | * 16 * * * * | 1 0 1 0 xx3oo3oo .. ..&#x ♦ 4 4 | 6 4 6 | 4 6 4 | 1 0 4 1 0 | * * 40 * * * | 0 2 0 0 xx3oo .. *b3oo ..&#x ♦ 4 4 | 6 4 6 | 4 6 4 | 0 1 4 0 1 | * * * 80 * * | 0 1 1 0 .x3.o3.o *b3.o .. ♦ 0 8 | 0 0 24 | 0 0 32 | 0 0 0 8 8 | * * * * 10 * | 0 1 0 1 .x3.o .. *b3.o3.o ♦ 0 5 | 0 0 10 | 0 0 10 | 0 0 0 0 5 | * * * * * 16 | 0 0 1 1 ---------------------+-------+----------+------------+-----------------+-------------------+---------- x.3o.3o. *b3o.3o. ♦ 16 0 | 80 0 0 | 160 0 0 | 40 80 0 0 0 | 10 16 0 0 0 0 | 1 * * * xx3oo3oo *b3oo ..&#x ♦ 8 8 | 24 8 24 | 32 24 32 | 8 8 32 8 8 | 1 0 8 8 1 0 | * 10 * * xx3oo .. *b3oo3oo&#x ♦ 5 5 | 10 5 10 | 10 10 10 | 0 5 10 0 5 | 0 1 0 5 0 1 | * * 16 * .x3.o3.o *b3.o3.o ♦ 0 16 | 0 0 80 | 0 0 160 | 0 0 0 40 80 | 0 0 0 0 10 16 | * * * 1
xx xo ox xo3oo3ox&#zx → height = 0 o. o. o. o.3o.3o. & | 32 | 1 1 3 6 | 1 3 3 6 9 18 | 3 1 9 18 3 12 8 6 | 1 3 12 8 6 3 5 2 | 3 5 2 1 ------------------------+----+-------------+-------------------+------------------------+-----------------------+--------- x. .. .. .. .. .. & | 2 | 16 * * * ♦ 1 3 0 6 0 0 | 3 0 9 18 0 0 0 0 | 1 3 12 8 6 0 0 0 | 3 5 2 0 .. x. .. .. .. .. & | 2 | * 16 * * | 1 0 0 0 6 0 | 0 0 6 0 3 6 0 0 | 0 3 6 0 0 3 2 0 | 3 2 0 1 .. .. .. x. .. .. & | 2 | * * 48 * | 0 1 2 0 0 4 | 2 1 0 4 0 2 4 2 | 1 0 2 4 2 1 2 2 | 1 2 2 1 oo oo oo oo3oo3oo&#x | 2 | * * * 96 | 0 0 0 1 2 4 | 0 0 2 4 1 4 2 2 | 0 1 4 2 2 2 2 1 | 2 2 1 1 ------------------------+----+-------------+-------------------+------------------------+-----------------------+--------- x. x. .. .. .. .. & | 4 | 2 2 0 0 | 8 * * * * * ♦ 0 0 6 0 0 0 0 0 | 0 3 6 0 0 0 0 0 | 3 2 0 0 x. .. .. x. .. .. & | 4 | 2 0 2 0 | * 24 * * * * ♦ 2 0 0 4 0 0 0 0 | 1 0 2 4 2 0 0 0 | 1 2 2 0 .. .. .. x.3o. .. & | 3 | 0 0 3 0 | * * 32 * * * | 1 1 0 0 0 0 2 0 | 1 0 0 2 0 0 1 2 | 0 1 2 1 xx .. .. .. .. ..&#x | 4 | 2 0 0 2 | * * * 48 * * ♦ 0 0 2 4 0 0 0 0 | 0 1 4 2 2 0 0 0 | 2 2 1 0 .. xo .. .. .. ..&#x & | 3 | 0 1 0 2 | * * * * 96 * | 0 0 1 0 1 2 0 0 | 0 1 2 0 0 2 1 0 | 2 1 0 1 .. .. .. xo .. ..&#x & | 3 | 0 0 1 2 | * * * * * 192 | 0 0 0 1 0 1 1 1 | 0 0 1 1 1 1 1 1 | 1 1 1 1 ------------------------+----+-------------+-------------------+------------------------+-----------------------+--------- x. .. .. x.3o. .. & ♦ 6 | 3 0 6 0 | 0 3 2 0 0 0 | 16 * * * * * * * | 1 0 0 2 0 0 0 0 | 0 1 2 0 .. .. .. x.3o.3o. & ♦ 4 | 0 0 6 0 | 0 0 4 0 0 0 | * 8 * * * * * * | 1 0 0 0 0 0 0 2 | 0 0 2 1 xx xo .. .. .. ..&#x & ♦ 6 | 3 2 0 4 | 1 0 0 2 2 0 | * * 48 * * * * * | 0 1 2 0 0 0 0 0 | 2 1 0 0 xx .. .. xo .. ..&#x & ♦ 6 | 3 0 2 4 | 0 1 0 2 0 2 | * * * 96 * * * * | 0 0 1 1 1 0 0 0 | 1 1 1 0 .. xo ox .. .. ..&#x ♦ 4 | 0 2 0 4 | 0 0 0 0 4 0 | * * * * 24 * * * | 0 1 0 0 0 2 0 0 | 2 0 0 1 .. xo .. .. .. ox&#x & ♦ 4 | 0 1 1 4 | 0 0 0 0 2 2 | * * * * * 96 * * | 0 0 1 0 0 1 1 0 | 1 1 0 1 .. .. .. xo3oo ..&#x & ♦ 4 | 0 0 3 3 | 0 0 1 0 0 3 | * * * * * * 64 * | 0 0 0 1 0 0 1 1 | 0 1 1 1 .. .. .. xo .. ox&#x ♦ 4 | 0 0 2 4 | 0 0 0 0 0 4 | * * * * * * * 48 | 0 0 0 0 1 1 0 1 | 1 0 1 1 ------------------------+----+-------------+-------------------+------------------------+-----------------------+--------- x. .. .. x.3o.3o. & ♦ 8 | 4 0 12 0 | 0 6 8 0 0 0 | 4 2 0 0 0 0 0 0 | 4 * * * * * * * | 0 0 2 0 xx xo ox .. .. ..&#x ♦ 8 | 4 4 0 8 | 2 0 0 4 8 0 | 0 0 4 0 2 0 0 0 | * 12 * * * * * * | 2 0 0 0 xx xo .. .. .. ox&#x & ♦ 8 | 4 2 2 8 | 1 1 0 4 4 4 | 0 0 2 2 0 2 0 0 | * * 48 * * * * * | 1 1 0 0 xx .. .. xo3oo ..&#x & ♦ 8 | 4 0 6 6 | 0 3 2 3 0 6 | 1 0 0 3 0 0 2 0 | * * * 32 * * * * | 0 1 1 0 xx .. .. xo .. ox&#x ♦ 8 | 4 0 4 8 | 0 2 0 4 0 8 | 0 0 0 4 0 0 0 2 | * * * * 24 * * * | 1 0 1 0 .. xo ox xo .. ox&#zx ♦ 8 | 0 4 4 16 | 0 0 0 0 16 16 | 0 0 0 0 4 8 0 4 | * * * * * 12 * * | 1 0 0 1 .. xo .. .. oo3ox&#x & ♦ 5 | 0 1 3 6 | 0 0 1 0 3 6 | 0 0 0 0 0 3 2 0 | * * * * * * 32 * | 0 1 0 1 .. .. .. xo3oo3ox&#x ♦ 8 | 0 0 12 12 | 0 0 8 0 0 24 | 0 2 0 0 0 0 8 6 | * * * * * * * 8 | 0 0 1 1 ------------------------+----+-------------+-------------------+------------------------+-----------------------+--------- xx xo ox xo .. ox&#zx ♦ 16 | 8 8 8 32 | 4 4 0 16 32 32 | 0 0 16 16 8 16 0 8 | 0 4 8 0 4 2 0 0 | 6 * * * xx xo .. .. oo3ox&#x & ♦ 10 | 5 2 6 12 | 1 3 2 6 6 12 | 1 0 3 6 0 6 4 0 | 0 0 3 2 0 0 2 0 | * 16 * * xx .. .. xo3oo3ox&#x ♦ 16 | 8 0 24 24 | 0 12 16 12 0 48 | 8 4 0 24 0 0 16 12 | 2 0 0 8 6 0 0 2 | * * 4 * .. xo ox xo3oo3ox&#zx ♦ 16 | 0 8 24 48 | 0 0 16 0 48 96 | 0 4 0 0 12 48 32 24 | 0 0 0 0 0 6 16 4 | * * * 2
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