- general duoprisms:
- 2n,2m-dip 2n,m-dip 4,n-dip n,m-dip 4,n/d-dip n/d,m/b-dip
- general polytopal classes:
- Wythoffian polychora segmentochora
links
| Acronym | 4,2n/d-dip |
| Name | square - 2n/d-gram duoprism |
| Circumradius | sqrt[1/2+1/(4 sin2(πd/2n))] |
| Face vector | 8n, 16n, 10n+4, 2n+4 |
| Especially | tes (n=2, d=1) shiddip (n=3, d=1) sodip (n=4, d=1) sistodip (n=4, d=3) squadedip (n=5, d=1) sitwadip (n=6, d=1) |
| Confer |
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External links |
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Incidence matrix according to Dynkin symbol
x4o x2n/do (n>2, d odd) . . . . | 8n | 2 2 | 1 4 1 | 2 2 -----------+----+-------+---------+----- x . . . | 2 | 8n * | 1 2 0 | 2 1 . . x . | 2 | * 8n | 0 2 1 | 1 2 -----------+----+-------+---------+----- x4o . . | 4 | 4 0 | 2n * * | 2 0 x . x . | 4 | 2 2 | * 8n * | 1 1 . . x2n/do | 2n | 0 2n | * * 4 | 0 2 -----------+----+-------+---------+----- x4o x . ♦ 8 | 8 4 | 2 4 0 | 2n * x . x2n/do ♦ 4n | 2n 4n | 0 2n 2 | * 4
x4o xn/dx (n>2, d odd) . . . . | 8n | 2 1 1 | 1 2 2 1 | 1 1 2 ----------+----+----------+------------+------ x . . . | 2 | 8n * * | 1 1 1 0 | 1 1 1 . . x . | 2 | * 4n * | 0 2 0 1 | 1 0 2 . . . x | 2 | * * 4n | 0 0 2 1 | 0 1 2 ----------+----+----------+------------+------ x4o . . | 4 | 4 0 0 | 2n * * * | 1 1 0 x . x . | 4 | 2 2 0 | * 4n * * | 1 0 1 x . . x | 4 | 2 0 2 | * * 4n * | 0 1 1 . . xn/dx | 2n | 0 n n | * * * 4 | 0 0 2 ----------+----+----------+------------+------ x4o x . ♦ 8 | 8 4 0 | 2 4 0 0 | n * * x4o . x ♦ 8 | 8 0 4 | 2 0 4 0 | * n * x . xn/dx ♦ 4n | 2n 2n 2n | 0 n n 2 | * * 4
x x x2n/do (n>2, d odd) . . . . | 8n | 1 1 2 | 1 2 2 1 | 2 1 1 -----------+----+----------+------------+------- x . . . | 2 | 4n * * | 1 2 0 0 | 2 1 0 . x . . | 2 | * 4n * | 1 0 2 0 | 2 0 1 . . x . | 2 | * * 8n | 0 1 1 1 | 1 1 1 -----------+----+----------+------------+------- x x . . | 4 | 2 2 0 | 2n * * * | 2 0 0 x . x . | 4 | 2 0 2 | * 4n * * | 1 1 0 . x x . | 4 | 0 2 2 | * * 4n * | 1 0 1 . . x2n/do | 2n | 0 0 2n | * * * 4 | 0 1 1 -----------+----+----------+------------+------- x x x . ♦ 8 | 4 4 4 | 2 2 2 0 | 2n * * x . x2n/do ♦ 4n | 2n 0 4n | 0 2n 0 2 | * 2 * . x x2n/do ♦ 4n | 0 2n 4n | 0 0 2n 2 | * * 2
x x xn/dx (n>2, d odd) . . . . | 8n | 1 1 1 1 | 1 1 1 1 1 1 | 1 1 1 1 ----------+----+-------------+------------------+-------- x . . . | 2 | 4n * * * | 1 1 1 0 0 0 | 1 1 1 0 . x . . | 2 | * 4n * * | 1 0 0 1 1 0 | 1 1 0 1 . . x . | 2 | * * 4n * | 0 1 0 1 0 1 | 1 0 1 1 . . . x | 2 | * * * 4n | 0 0 1 0 1 1 | 0 1 1 1 ----------+----+-------------+------------------+-------- x x . . | 4 | 2 2 0 0 | 2n * * * * * | 1 1 0 0 x . x . | 4 | 2 0 2 0 | * 2n * * * * | 1 0 1 0 x . . x | 4 | 2 0 0 2 | * * 2n * * * | 0 1 1 0 . x x . | 4 | 0 2 2 0 | * * * 2n * * | 1 0 0 1 . x . x | 4 | 0 2 0 2 | * * * * 2n * | 0 1 0 1 . . xn/dx | 2n | 0 0 n n | * * * * * 4 | 0 0 1 1 ----------+----+-------------+------------------+-------- x x x . ♦ 8 | 4 4 4 0 | 2 2 0 2 0 0 | n * * * x x . x ♦ 8 | 4 4 0 4 | 2 0 2 0 2 0 | * n * * x . xn/dx ♦ 4n | 2n 0 2n 2n | 0 n n 0 0 2 | * * 2 * . x xn/dx ♦ 4n | 0 2n 2n 2n | 0 0 0 n n 2 | * * * 2
xx xx2n/doo&#x (n>2, d odd) → height = 1
({2n/d}-p || {2n/d}-p)
o. o.2n/do. | 4n * | 1 2 1 0 0 | 2 1 1 2 0 0 | 1 2 1 0
.o .o2n/d.o | * 4n | 0 0 1 1 2 | 0 0 1 2 2 1 | 0 2 1 1
---------------+-------+----------------+-----------------+---------
x. .. .. | 2 0 | 2n * * * * | 2 0 1 0 0 0 | 1 2 0 0
.. x. .. | 2 0 | * 4n * * * | 1 1 0 1 0 0 | 1 1 1 0
oo oo2n/doo&#x | 1 1 | * * 4n * * | 0 0 1 2 0 0 | 0 2 1 0
.x .. .. | 0 2 | * * * 2n * | 0 0 1 0 2 0 | 0 2 0 1
.. .x .. | 0 2 | * * * * 4n | 0 0 0 1 1 1 | 0 1 1 1
---------------+-------+----------------+-----------------+---------
x. x. .. | 4 0 | 2 2 0 0 0 | 2n * * * * * | 1 1 0 0
.. x.2n/do. | 2n 0 | 0 2n 0 0 0 | * 2 * * * * | 1 0 1 0
xx .. ..&#x | 2 2 | 1 0 2 1 0 | * * 2n * * * | 0 2 0 0
.. xx ..&#x | 2 2 | 0 1 2 0 1 | * * * 4n * * | 0 1 1 0
.x .x .. | 0 4 | 0 0 0 2 2 | * * * * 2n * | 0 1 0 1
.. .x2/dn.o | 0 2n | 0 0 0 0 2n | * * * * * 2 | 0 0 1 1
---------------+-------+----------------+-----------------+---------
x. x.2n/do. ♦ 4n 0 | 2n 4n 0 0 0 | 2n 2 0 0 0 0 | 1 * * *
xx xx ..&#x ♦ 4 4 | 2 2 4 2 2 | 1 0 2 2 1 0 | * 2n * *
.. xx2n/doo&#x ♦ 2n 2n | 0 2n 2n 0 2n | 0 1 0 2n 0 1 | * * 2 *
.x .x2n/d.o ♦ 0 4n | 0 0 0 2n 4n | 0 0 0 0 2n 2 | * * * 1
xx xxn/dxx&#x (n>2, d odd) → height = 1
({2n/d}-p || {2n/d}-p)
o. o. o. | 4n * | 1 1 1 1 0 0 0 | 1 1 1 1 1 1 0 0 0 | 1 1 1 1 0
.o .o .o | * 4n | 0 0 0 1 1 1 1 | 0 0 0 1 1 1 1 1 1 | 0 1 1 1 1
--------------+-------+----------------------+----------------------+----------
x. .. .. | 2 0 | 2n * * * * * * | 1 1 0 1 0 0 0 0 0 | 1 1 1 0 0
.. x. .. | 2 0 | * 2n * * * * * | 1 0 1 0 1 0 0 0 0 | 1 1 0 1 0
.. .. x. | 2 0 | * * 2n * * * * | 0 1 1 0 0 1 0 0 0 | 1 0 1 1 0
oo oon/doo&#x | 1 1 | * * * 4n * * * | 0 0 0 1 1 1 0 0 0 | 0 1 1 1 0
.x .. .. | 0 2 | * * * * 2n * * | 0 0 0 1 0 0 1 1 0 | 0 1 1 0 1
.. .x .. | 0 2 | * * * * * 2n * | 0 0 0 0 1 0 1 0 1 | 0 1 0 1 1
.. .. .x | 0 2 | * * * * * * 2n | 0 0 0 0 0 1 0 1 1 | 0 0 1 1 1
--------------+-------+----------------------+----------------------+----------
x. x. .. | 4 0 | 2 2 0 0 0 0 0 | n * * * * * * * * | 1 1 0 0 0
x. .. x. | 4 0 | 2 0 2 0 0 0 0 | * n * * * * * * * | 1 0 1 0 0
.. x.n/dx. | 2n 0 | 0 3 3 0 0 0 0 | * * 2 * * * * * * | 1 0 0 1 0
xx .. ..&#x | 2 2 | 1 0 0 2 1 0 0 | * * * 2n * * * * * | 0 1 1 0 0
.. xx ..&#x | 2 2 | 0 1 0 2 0 1 0 | * * * * 2n * * * * | 0 1 0 1 0
.. .. xx&#x | 2 2 | 0 0 1 2 0 0 1 | * * * * * 2n * * * | 0 0 1 1 0
.x .x .. | 0 4 | 0 0 0 0 2 2 0 | * * * * * * n * * | 0 1 0 0 1
.x .. .x | 0 4 | 0 0 0 0 2 0 2 | * * * * * * * n * | 0 0 1 0 1
.. .xn/d.x | 0 2n | 0 0 0 0 0 3 3 | * * * * * * * * 2 | 0 0 0 1 1
--------------+-------+----------------------+----------------------+----------
x. x.n/dx. ♦ 4n 0 | 2n 2n 2n 0 0 0 0 | n n 2 0 0 0 0 0 0 | 1 * * * *
xx xx ..&#x ♦ 4 4 | 2 2 0 4 2 2 0 | 1 0 0 2 2 0 1 0 0 | * n * * *
xx .. xx&#x ♦ 4 4 | 2 0 2 4 2 0 2 | 0 1 0 2 0 2 0 1 0 | * * n * *
.. xxn/dxx&#x ♦ 2n 2n | 0 n n 2n 0 n n | 0 0 1 0 3 3 0 0 1 | * * * 2 *
.x .xn/d.x ♦ 0 4n | 0 0 0 0 2n 2n 2n | 0 0 0 0 0 0 n n 2 | * * * * 1
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