Acronym | triddit |
Name |
triangle duotegum, dual of triangle duoprism, 6-2-stepprism |
Circumradius | 1/sqrt(2) = 0.707107 |
Dual | triddip |
Face vector | 6, 15, 18, 9 |
Confer |
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External links |
This polychoron can be obtained as the convex hull of the 2 fully orthogonal a-triangles.
Metric sizes in here are given such that the lacing edge becomes unity.
Incidence matrix according to Dynkin symbol
m3o2m3o = ao3oo oa3oo&#zx → height = 0, where a = sqrt(3/2) = 1.224745 o.3o. o.3o. | 3 * ♦ 2 3 0 | 6 3 | 6 .o3.o .o3.o | * 3 ♦ 0 3 2 | 3 6 | 6 ----------------+-----+-------+-----+-- a. .. .. .. | 2 0 | 3 * * | 3 0 | 3 oo3oo oo3oo&#x | 1 1 | * 9 * | 2 2 | 4 .. .. .a .. | 0 2 | * * 3 | 0 3 | 3 ----------------+-----+-------+-----+-- ao .. .. ..&#x | 2 1 | 1 2 0 | 9 * | 2 .. .. oa ..&#x | 1 2 | 0 2 1 | * 9 | 2 ----------------+-----+-------+-----+-- ao .. oa ..&#x | 2 2 | 1 4 1 | 2 2 | 9
or o.3o. o.3o. & | 6 ♦ 2 3 | 9 | 6 ------------------+---+-----+----+-- a. .. .. .. & | 2 | 6 * | 3 | 3 oo3oo oo3oo&#x | 2 | * 9 | 4 | 4 ------------------+---+-----+----+-- ao .. .. ..&#x & | 3 | 1 2 | 18 | 2 ------------------+---+-----+----+-- ao .. oa ..&#x | 4 | 2 4 | 4 | 9
ooa oao3ooo&#xt → height(1,2) = 1/sqrt(3) = 0.577350, height(2,3) = 1/sqrt(12) = 0.288675, a = sqrt(3/2) = 1.224745 (pt || pseudo a-{3} || perp a-line) o.. o..3o.. | 1 * * ♦ 3 2 0 0 0 | 3 6 0 0 | 6 0 .o. .o.3.o. | * 3 * ♦ 1 0 2 2 0 | 2 2 1 4 | 4 2 ..o ..o3..o | * * 2 ♦ 0 1 0 3 1 | 0 3 3 3 | 3 3 -------------------+-------+-----------+---------+---- oo. oo.3oo.&#x | 1 1 0 | 3 * * * * | 2 2 0 0 | 4 0 o.o o.o3o.o&#a | 1 0 1 | * 2 * * * | 0 3 0 0 | 3 0 ... .a. ... | 0 2 0 | * * 3 * * | 1 0 0 2 | 2 1 .oo .oo3.oo&#x | 0 1 1 | * * * 6 * | 0 1 1 2 | 2 2 ..a ... ... | 0 0 2 | * * * * 1 | 0 0 3 0 | 0 3 -------------------+-------+-----------+---------+---- ... oa. ...&#x | 1 2 0 | 2 0 1 0 0 | 3 * * * | 2 0 ooo ooo3ooo&#(axx) | 1 1 1 | 1 1 0 1 0 | * 6 * * | 2 0 .oa ... ...&#x | 0 1 2 | 0 0 0 2 1 | * * 3 * | 0 2 ... .ao ...&#x | 0 2 1 | 0 0 1 2 0 | * * * 6 | 1 1 -------------------+-------+-----------+---------+---- ... oao ...&#(ax) | 1 2 1 | 2 1 1 2 0 | 1 2 0 1 | 6 * .oa .ao ...&#x | 0 2 2 | 0 0 1 4 1 | 0 0 2 2 | * 3
oaoo ooao&#(ax) → height(1,2) = height(3,4) = sqrt(5/8) = 0.790569, laced x height(1,3) = height(2,4) = 3/sqrt(8) = 1.060660, laced a height(2,3) = 1/2, laced x height(1,4) = 1 a = sqrt(3/2) = 1.224745 o... o... | 1 * * * ♦ 2 2 1 0 0 0 0 0 | 1 4 2 2 0 0 0 0 | 2 4 0 0 .o.. .o.. | * 2 * * ♦ 1 0 0 1 2 1 0 0 | 1 2 1 0 2 1 2 0 | 2 2 1 1 ..o. ..o. | * * 2 * ♦ 0 1 0 0 2 0 1 1 | 0 2 0 1 1 2 2 1 | 1 2 1 2 ...o ...o | * * * 1 ♦ 0 0 1 0 0 2 0 2 | 0 0 2 2 0 0 4 1 | 0 4 0 2 -----------------+---------+-----------------+-----------------+-------- oo.. oo..&#x | 1 1 0 0 | 2 * * * * * * * | 1 2 1 0 0 0 0 0 | 2 2 0 0 o.o. o.o.&#a | 1 0 1 0 | * 2 * * * * * * | 0 2 0 1 0 0 0 0 | 1 2 0 0 o..o o..o&#x | 1 0 0 1 | * * 1 * * * * * | 0 0 2 2 0 0 0 0 | 0 4 0 0 .a.. .... | 0 2 0 0 | * * * 1 * * * * | 1 0 0 0 2 0 0 0 | 2 0 1 0 .oo. .oo.&#x | 0 1 1 0 | * * * * 4 * * * | 0 1 0 0 1 1 1 0 | 1 1 1 1 .o.o .o.o&#a | 0 1 0 1 | * * * * * 2 * * | 0 0 1 0 0 0 2 0 | 0 2 0 1 .... ..a. | 0 0 2 0 | * * * * * * 1 * | 0 0 0 0 0 2 0 1 | 0 0 1 2 ..oo ..oo&#x | 0 0 1 1 | * * * * * * * 2 | 0 0 0 1 0 0 2 1 | 0 2 0 2 -----------------+---------+-----------------+-----------------+-------- oa.. ....&#x | 1 2 0 0 | 2 0 0 1 0 0 0 0 | 1 * * * * * * * | 2 0 0 0 ooo. ooo.&#(axx) | 1 1 1 0 | 1 1 0 0 1 0 0 0 | * 4 * * * * * * | 1 1 0 0 oo.o oo.o&#(axx) | 1 1 0 1 | 1 0 1 0 0 1 0 0 | * * 2 * * * * * | 0 2 0 0 o.oo o.oo&#(axx) | 1 0 1 1 | 0 1 1 0 0 0 0 1 | * * * 2 * * * * | 0 2 0 0 .ao. ....&#(axx) | 0 2 1 0 | 0 0 0 1 2 0 0 0 | * * * * 2 * * * | 1 0 1 0 .... .oa.&#(axx) | 0 1 2 0 | 0 0 0 0 2 0 1 0 | * * * * * 2 * * | 0 0 1 1 .ooo .ooo&#(axx) | 0 1 1 1 | 0 0 0 0 1 1 0 1 | * * * * * * 4 * | 0 1 0 1 .... ..ao&#x | 0 0 2 1 | 0 0 0 0 0 0 1 2 | * * * * * * * 1 | 0 0 0 2 -----------------+---------+-----------------+-----------------+-------- oao. ....&#(ax) | 1 2 1 0 | 2 1 0 1 2 0 0 0 | 1 2 0 0 1 0 0 0 | 2 * * * oooo oooo&#(ax) | 1 1 1 1 | 1 1 1 0 1 1 0 1 | 0 1 1 1 0 0 1 0 | * 4 * * .ao. .oa.&#x | 0 2 2 0 | 0 0 0 1 4 0 1 0 | 0 0 0 0 2 2 0 0 | * * 1 * .... .oao&#(ax) | 0 1 2 1 | 0 0 0 0 2 1 1 2 | 0 0 0 0 0 1 2 1 | * * * 2
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