Acronym | 6,n-dip |
Name | hexagon - n-gonal duoprism |
Circumradius | sqrt[1+1/(4 sin2(π/n))] |
General of army | (is itself convex) |
Colonel of regiment | (is itself locally convex) |
Face vector | 6n, 12n, 7n+6, n+6 |
Especially | thiddip (n=3) shiddip (n=4) phiddip (n=5) hiddip (n=6) hodip (n=8) hadedip (n=10) hitwadip (n=12) |
Confer |
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External links |
Incidence matrix according to Dynkin symbol
x6o xno (n>2) . . . . | 6n | 2 2 | 1 4 1 | 2 2 --------+----+-------+--------+---- x . . . | 2 | 6n * | 1 2 0 | 2 1 . . x . | 2 | * 6n | 0 2 1 | 1 2 --------+----+-------+--------+---- x6o . . | 6 | 6 0 | n * * | 2 0 x . x . | 4 | 2 2 | * 6n * | 1 1 . . xno | n | 0 n | * * 6 | 0 2 --------+----+-------+--------+---- x6o x . ♦ 12 | 12 6 | 2 6 0 | n * x . xno ♦ 2n | n 2n | 0 n 2 | * 6
x3x xno (n>2) . . . . | 6n | 1 1 2 | 1 2 2 1 | 2 1 1 --------+----+----------+-----------+------ x . . . | 2 | 3n * * | 1 2 0 0 | 2 1 0 . x . . | 2 | * 3n * | 1 0 2 0 | 2 0 1 . . x . | 2 | * * 6n | 0 1 1 1 | 1 1 1 --------+----+----------+-----------+------ x3x . . | 6 | 3 3 0 | n * * * | 2 0 0 x . x . | 4 | 2 0 2 | * 3n * * | 1 1 0 . x x . | 4 | 0 2 2 | * * 3n * | 1 0 1 . . xno | n | 0 0 n | * * * 6 | 0 1 1 --------+----+----------+-----------+------ x3x x . ♦ 12 | 6 6 6 | 2 3 3 0 | n * * x . xno ♦ 2n | n 0 2n | 0 n 0 2 | * 3 * . x xno ♦ 2n | 0 n 2n | 0 0 n 2 | * * 3
x3x sns (n>2) . . demi( . . ) | 6n | 1 1 2 | 1 2 2 1 | 2 1 1 ----------------+----+----------+-----------+------ x . demi( . . ) | 2 | 3n * * | 1 2 0 0 | 2 1 0 . x demi( . . ) | 2 | * 3n * | 1 0 2 0 | 2 0 1 . . sefa( sns ) | 2 | * * 6n | 0 1 1 1 | 1 1 1 ----------------+----+----------+-----------+------ x3x demi( . . ) | 6 | 3 3 0 | n * * * | 2 0 0 x . sefa( sns ) | 4 | 2 0 2 | * 3n * * | 1 1 0 . x sefa( sns ) | 4 | 0 2 2 | * * 3n * | 1 0 1 . . sns ♦ n | 0 0 n | * * * 6 | 0 1 1 ----------------+----+----------+-----------+------ x3x sefa( sns ) ♦ 12 | 6 6 6 | 2 3 3 0 | n * * x . sns ♦ 2n | n 0 2n | 0 n 0 2 | * 3 * . x sns ♦ 2n | 0 n 2n | 0 0 n 2 | * * 3
xux xxxnooo&#xt (n>2) → both heights = sqrt(3)/2 = 0.866025 (n-p || pseudo (x,u)-n-p || n-p) o.. o..no.. | 2n * * | 1 2 1 0 0 0 0 | 2 1 2 1 0 0 0 0 | 1 1 2 0 0 .o. .o.n.o. | * 2n * | 0 0 1 2 1 0 0 | 0 0 2 1 1 2 0 0 | 0 1 2 1 0 ..o ..on..o | * * 2n | 0 0 0 0 1 1 2 | 0 0 0 1 0 2 2 1 | 0 0 2 1 1 ----------------+----------+--------------------+-------------------+---------- x.. ... ... | 2 0 0 | n * * * * * * | 2 0 0 1 0 0 0 0 | 1 0 2 0 0 ... x.. ... | 2 0 0 | * 2n * * * * * | 1 1 1 0 0 0 0 0 | 1 1 1 0 0 oo. oo.noo.&#x | 1 1 0 | * * 2n * * * * | 0 0 2 1 0 0 0 0 | 0 1 2 0 0 ... .x. ... | 0 2 0 | * * * 2n * * * | 0 0 1 0 1 1 0 0 | 0 1 1 1 0 .oo .oon.oo&#x | 0 1 1 | * * * * 2n * * | 0 0 0 1 0 2 0 0 | 0 0 2 1 0 ..x ... ... | 0 0 2 | * * * * * n * | 0 0 0 1 0 0 2 0 | 0 0 2 0 1 ... ..x ... | 0 0 2 | * * * * * * 2n | 0 0 0 0 0 1 1 1 | 0 0 1 1 1 ----------------+----------+--------------------+-------------------+---------- x.. x.. ... | 4 0 0 | 2 2 0 0 0 0 0 | n * * * * * * * | 1 0 1 0 0 ... x..no.. | n 0 0 | 0 n 0 0 0 0 0 | * 2 * * * * * * | 1 1 0 0 0 ... xx. ...&#x | 2 2 0 | 0 1 2 1 0 0 0 | * * 2n * * * * * | 0 1 1 0 0 xux ... ...&#xt | 2 2 2 | 1 0 2 0 2 1 0 | * * * n * * * * | 0 0 2 0 0 ... .x.n.o. | 0 n 0 | 0 0 0 n 0 0 0 | * * * * 2 * * * | 0 1 0 1 0 ... .xx ...&#x | 0 2 2 | 0 0 0 1 2 0 1 | * * * * * 2n * * | 0 0 1 1 0 ..x ..x ... | 0 0 4 | 0 0 0 0 0 2 2 | * * * * * * n * | 0 0 1 0 1 ... ..xn..o | 0 0 n | 0 0 0 0 0 0 n | * * * * * * * 2 | 0 0 0 1 1 ----------------+----------+--------------------+-------------------+---------- x.. x..no.. ♦ 2n 0 0 | n 2n 0 0 0 0 0 | n 2 0 0 0 0 0 0 | 1 * * * * ... xx.noo.&#x ♦ n n 0 | 0 n n n 0 0 0 | 0 1 n 0 1 0 0 0 | * 2 * * * xux xxx ...&#xt ♦ 4 4 4 | 2 2 4 2 4 2 2 | 1 0 2 2 0 2 1 0 | * * n * * ... .xxn.oo&#x ♦ 0 n n | 0 0 0 n n 0 n | 0 0 0 0 1 n 0 1 | * * * 2 * ..x ..xn..o ♦ 0 0 2n | 0 0 0 0 0 n 2n | 0 0 0 0 0 0 n 2 | * * * * 1
or o.. o..no.. & | 4n * | 1 2 1 0 | 2 1 2 1 0 | 1 1 2 .o. .o.n.o. | * 2n | 0 0 2 2 | 0 0 4 1 1 | 0 2 2 -------------------+-------+-------------+-------------+------ x.. ... ... & | 2 0 | 2n * * * | 2 0 0 1 0 | 1 0 2 ... x.. ... & | 2 0 | * 4n * * | 1 1 1 0 0 | 1 1 1 oo. oo.noo.&#x & | 1 1 | * * 4n * | 0 0 2 1 0 | 0 1 2 ... .x. ... | 0 2 | * * * 2n | 0 0 2 0 1 | 0 2 1 -------------------+-------+-------------+-------------+------ x.. x.. ... & | 4 0 | 2 2 0 0 | 2n * * * * | 1 0 1 ... x..no.. & | n 0 | 0 n 0 0 | * 4 * * * | 1 1 0 ... xx. ...&#x & | 2 2 | 0 1 2 1 | * * 4n * * | 0 1 1 xux ... ...&#xt | 4 2 | 2 0 4 0 | * * * n * | 0 0 2 ... .x.n.o. | 0 n | 0 0 0 n | * * * * 2 | 0 2 0 -------------------+-------+-------------+-------------+------ x.. x..no.. & ♦ 2n 0 | n 2n 0 0 | n 2 0 0 0 | 2 * * ... xx.noo.&#x & ♦ n n | 0 n n n | 0 1 n 0 1 | * 4 * xux xxx ...&#xt ♦ 8 4 | 4 4 8 2 | 2 0 4 2 0 | * * n
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