| Acronym | n,cube-dip |
| Name | n-gon - cube duoprism |
| Circumradius | sqrt[3/4+1/(4 sin2(π/n))] |
| Face vector | 8n, 20n, 18n+8, 7n+12, n+6 |
| Especially | tracube (n=3) pent (n=4) pecube (n=5) hacube (n=6) ocube (n=8) dacube (n=10) twacube (n=12) |
| Confer |
|
Incidence matrix according to Dynkin symbol
xno o3o4x (n>2) . . . . . | 8n | 2 3 | 1 6 3 | 3 6 1 | 3 2 ----------+----+--------+----------+---------+---- x . . . . | 2 | 8n * | 1 3 0 | 3 3 0 | 3 1 . . . . x | 2 | * 12n | 0 2 2 | 1 4 1 | 2 2 ----------+----+--------+----------+---------+---- xno . . . | n | n 0 | 8 * * | 3 0 0 | 3 0 x . . . x | 4 | 2 2 | * 12n * | 1 2 0 | 2 1 . . . o4x | 4 | 0 4 | * * 6n | 0 2 1 | 1 2 ----------+----+--------+----------+---------+---- xno . . x ♦ 2n | 2n n | 2 n 0 | 12 * * | 2 0 x . . o4x ♦ 8 | 4 8 | 0 4 2 | * 6n * | 1 1 . . o3o4x ♦ 8 | 0 12 | 0 0 6 | * * n | 0 2 ----------+----+--------+----------+---------+---- xno . o4x ♦ 4n | 4n 4n | 4 4n n | 4 n 0 | 6 * x . o3o4x ♦ 16 | 8 24 | 0 12 12 | 0 6 2 | * n
x x4o xno (n>2) . . . . . | 8n | 1 2 2 | 2 2 1 4 1 | 1 4 1 2 2 | 2 2 1 ----------+----+----------+---------------+-------------+------ x . . . . | 2 | 4n * * | 2 2 0 0 0 | 1 4 1 0 0 | 2 2 0 . x . . . | 2 | * 8n * | 1 0 1 2 0 | 1 2 0 2 1 | 2 1 1 . . . x . | 2 | * * 8n | 0 1 0 2 1 | 0 2 1 1 2 | 1 2 1 ----------+----+----------+---------------+-------------+------ x x . . . | 4 | 2 2 0 | 4n * * * * | 1 2 0 0 0 | 2 1 0 x . . x . | 4 | 2 0 2 | * 4n * * * | 0 2 1 0 0 | 1 2 0 . x4o . . | 4 | 0 4 0 | * * 2n * * | 1 0 0 2 0 | 2 0 1 . x . x . | 4 | 0 2 2 | * * * 8n * | 0 1 0 1 1 | 1 1 1 . . . xno | n | 0 0 n | * * * * 8 | 0 0 1 0 2 | 0 2 1 ----------+----+----------+---------------+-------------+------ x x4o . . ♦ 8 | 4 8 0 | 4 0 2 0 0 | n * * * * | 2 0 0 x x . x . ♦ 8 | 4 4 4 | 2 2 0 2 0 | * 4n * * * | 1 1 0 x . . xno ♦ 2n | n 0 2n | 0 n 0 0 2 | * * 4 * * | 0 2 0 . x4o x . ♦ 8 | 0 8 4 | 0 0 2 4 0 | * * * 2n * | 1 0 1 . x . xno ♦ 2n | 0 n 2n | 0 0 0 n 2 | * * * * 8 | 0 1 1 ----------+----+----------+---------------+-------------+------ x x4o x . ♦ 16 | 8 16 8 | 8 4 4 8 0 | 2 4 0 2 0 | n * * x x . xno ♦ 4n | 2n 2n 4n | n 2n 0 2n 4 | 0 n 2 0 2 | * 4 * . x4o xno ♦ 4n | 0 4n 4n | 0 0 n 4n 4 | 0 0 0 n 4 | * * 2
x x x xno (n>2) . . . . . | 8n | 1 1 1 2 | 1 1 2 1 2 2 1 | 1 2 2 1 2 1 1 | 2 1 1 1 ----------+----+-------------+---------------------+------------------+-------- x . . . . | 2 | 4n * * * | 1 1 2 0 0 0 0 | 1 2 2 1 0 0 0 | 2 1 1 0 . x . . . | 2 | * 4n * * | 1 0 0 1 2 0 0 | 1 2 0 0 2 1 0 | 2 1 0 1 . . x . . | 2 | * * 4n * | 0 1 0 1 0 2 0 | 1 0 2 0 2 0 1 | 2 0 1 1 . . . x . | 2 | * * * 8n | 0 0 1 0 1 1 1 | 0 1 1 1 1 1 1 | 1 1 1 1 ----------+----+-------------+---------------------+------------------+-------- x x . . . | 4 | 2 2 0 0 | 2n * * * * * * | 1 2 0 0 0 0 0 | 2 1 0 0 x . x . . | 4 | 2 0 2 0 | * 2n * * * * * | 1 0 2 0 0 0 0 | 2 0 1 0 x . . x . | 4 | 2 0 0 2 | * * 4n * * * * | 0 1 1 1 0 0 0 | 1 1 1 0 . x x . . | 4 | 0 2 2 0 | * * * 2n * * * | 1 0 0 0 2 0 0 | 2 0 0 1 . x . x . | 4 | 0 2 0 2 | * * * * 4n * * | 0 1 0 0 1 1 0 | 1 1 0 1 . . x x . | 4 | 0 0 2 2 | * * * * * 4n * | 0 0 1 0 1 0 1 | 1 0 1 1 . . . xno | n | 0 0 0 n | * * * * * * 8 | 0 0 0 1 0 1 1 | 0 1 1 1 ----------+----+-------------+---------------------+------------------+-------- x x x . . ♦ 8 | 4 4 4 0 | 2 2 0 2 0 0 0 | n * * * * * * | 2 0 0 0 x x . x . ♦ 8 | 4 4 0 4 | 2 0 2 0 2 0 0 | * 2n * * * * * | 1 1 0 0 x . x x . ♦ 8 | 4 0 4 4 | 0 2 2 0 0 2 0 | * * 2n * * * * | 1 0 1 0 x . . xno ♦ 2n | n 0 0 2n | 0 0 n 0 0 0 2 | * * * 4 * * * | 0 1 1 0 . x x x . ♦ 8 | 0 4 4 4 | 0 0 0 2 2 2 0 | * * * * 2n * * | 1 0 0 1 . x . xno ♦ 2n | 0 n 0 2n | 0 0 0 0 n 0 2 | * * * * * 4 * | 0 1 0 1 . . x xno ♦ 2n | 0 0 n 2n | 0 0 0 0 0 n 2 | * * * * * * 4 | 0 0 1 1 ----------+----+-------------+---------------------+------------------+-------- x x x x . ♦ 16 | 8 8 8 8 | 4 4 4 4 4 4 0 | 2 2 2 0 2 0 0 | n * * * x x . xno ♦ 4n | 2n 2n 0 4n | n 0 2n 0 2n 0 4 | 0 n 0 2 0 2 0 | * 2 * * x . x xno ♦ 4n | 2n 0 2n 4n | 0 n 2n 0 0 2n 4 | 0 0 n 2 0 0 2 | * * 2 * . x x xno ♦ 4n | 0 2n 2n 4n | 0 0 0 n 2n 2n 4 | 0 0 0 0 n 2 2 | * * * 2
xx4oo xxnoo&#x (n>2) → height = 1
({4}{n}-dip || {4}{n}-dip)
o.4o. o.no. | 4n * | 2 2 1 0 0 | 1 4 1 2 2 0 0 0 | 2 2 1 4 1 0 0 | 1 2 2 0
.o4.o .on.o | * 4n | 0 0 1 2 2 | 0 0 0 2 2 1 4 1 | 0 0 1 4 1 2 2 | 0 2 2 1
---------------+-------+----------------+---------------------+----------------+--------
x. .. .. .. | 2 0 | 4n * * * * | 1 2 0 1 0 0 0 0 | 2 1 1 2 0 0 0 | 1 2 1 0
.. .. x. .. | 2 0 | * 4n * * * | 0 2 1 0 1 0 0 0 | 1 2 0 2 1 0 0 | 1 1 2 0
oo4oo oonoo&#x | 1 1 | * * 4n * * | 0 0 0 2 2 0 0 0 | 0 0 1 4 1 0 0 | 0 2 2 0
.x .. .. .. | 0 2 | * * * 4n * | 0 0 0 1 0 1 2 0 | 0 0 1 2 0 2 1 | 0 2 1 1
.. .. .x .. | 0 2 | * * * * 4n | 0 0 0 0 1 0 2 1 | 0 0 0 2 1 1 2 | 0 1 2 1
---------------+-------+----------------+---------------------+----------------+--------
x.4o. .. .. | 4 0 | 4 0 0 0 0 | n * * * * * * * | 2 0 1 0 0 0 0 | 1 2 0 0
x. .. x. .. | 4 0 | 2 2 0 0 0 | * 4n * * * * * * | 1 1 0 1 0 0 0 | 1 1 1 0
.. .. x.no. | n 0 | 0 n 0 0 0 | * * 4 * * * * * | 0 2 0 0 1 0 0 | 1 0 2 0
xx .. .. ..&#x | 2 2 | 1 0 2 1 0 | * * * 4n * * * * | 0 0 1 2 0 0 0 | 0 2 1 0
.. .. xx ..&#x | 2 2 | 0 1 2 0 1 | * * * * 4n * * * | 0 0 0 2 1 0 0 | 0 1 2 0
.x4.o .. .. | 0 4 | 0 0 0 4 0 | * * * * * n * * | 0 0 1 0 0 2 0 | 0 2 0 1
.x .. .x .. | 0 4 | 0 0 0 2 2 | * * * * * * 4n * | 0 0 0 1 0 1 1 | 0 1 1 1
.. .. .xn.o | 0 n | 0 0 0 0 n | * * * * * * * 4 | 0 0 0 0 1 0 2 | 0 0 2 1
---------------+-------+----------------+---------------------+----------------+--------
x.4o. x. .. ♦ 8 0 | 8 4 0 0 0 | 2 4 0 0 0 0 0 0 | n * * * * * * | 1 1 0 0
x. .. x.no. ♦ 2n 0 | n 2n 0 0 0 | 0 n 2 0 0 0 0 0 | * 4 * * * * * | 1 0 1 0
xx4oo .. ..&#x ♦ 4 4 | 4 0 4 4 0 | 1 0 0 4 0 1 0 0 | * * n * * * * | 0 2 0 0
xx .. xx ..&#x ♦ 4 4 | 2 2 4 2 2 | 0 1 0 2 2 0 1 0 | * * * 4n * * * | 0 1 1 0
.. .. xxnoo&#x ♦ n n | 0 n n 0 n | 0 0 1 0 n 0 0 1 | * * * * 4 * * | 0 0 2 0
.x4.o .x .. ♦ 0 8 | 0 0 0 8 4 | 0 0 0 0 0 2 4 0 | * * * * * n * | 0 1 0 1
.x .. .xn.o ♦ 0 2n | 0 0 0 n 2n | 0 0 0 0 0 0 n 2 | * * * * * * 4 | 0 0 1 1
---------------+-------+----------------+---------------------+----------------+--------
x.4o. x.no. ♦ 4n 0 | 4n 4n 0 0 0 | n 4n 4 0 0 0 0 0 | n 4 0 0 0 0 0 | 1 * * *
xx4oo xx ..&#x ♦ 8 8 | 8 4 8 8 4 | 2 4 0 8 4 2 4 0 | 1 0 2 4 0 1 0 | * n * *
xx .. xxnoo&#x ♦ 2n 2n | n 2n 2n n 2n | 0 n 2 n 2n 0 n 2 | 0 1 0 n 2 0 1 | * * 4 *
.x4.o .xn.o ♦ 0 4n | 0 0 0 4n 4n | 0 0 0 0 0 n 4n 4 | 0 0 0 0 0 n 4 | * * * 1
© 2004-2024 | top of page |