triangular duotegmatic icosateron,
triangular duotegmatic alterprism,
dodecateron dual
- general polytopal classes:
- Catalan polytera
links
| Acronym | bidot |
| Name |
bidodecateron, triangular duotegmatic icosateron, triangular duotegmatic alterprism, dodecateron dual |
| Circumradius | sqrt(5/8) = 0.790569 |
| Inradius | 1/2 |
| Dual | dot |
| Face vector | 12, 60, 120, 90, 20 |
| Confer |
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External links |
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This polyteron can be obtained as the convex hull of the 2 hix compound (stade). Here all the edges of the former remain as long ones, while the short ones come in as interconnections of the 2 vertex set members. Each cell then joins a pair of adjacent vertices of one set to a pair of adjacent vertices of the other set, thus being a disphenoid. And the 4-elements are the duals of triddip.
Incidence matrix according to Dynkin symbol
o3o3m3o3o = ao3oo3oo3oo3oa&#zx → height = 0, where a = sqrt(3/2) = 1.224745 o.3o.3o.3o.3o. | 6 * ♦ 5 5 0 | 20 10 | 30 | 10 .o3.o3.o3.o3.o | * 6 ♦ 0 5 5 | 10 20 | 30 | 10 -------------------+-----+----------+-------+----+--- a. .. .. .. .. | 2 0 | 15 * * ♦ 4 0 | 6 | 4 oo3oo3oo3oo3oo&#x | 1 1 | * 30 * ♦ 4 4 | 12 | 6 .. .. .. .. .a | 0 2 | * * 15 ♦ 0 4 | 6 | 4 -------------------+-----+----------+-------+----+--- ao .. .. .. ..&#x | 2 1 | 1 2 0 | 60 * | 3 | 3 .. .. .. .. oa&#x | 1 2 | 0 2 1 | * 60 | 3 | 3 -------------------+-----+----------+-------+----+--- ao .. .. .. oa&#x | 2 2 | 1 4 1 | 2 2 | 90 | 2 -------------------+-----+----------+-------+----+--- ao3oo .. oo3oa&#zx ♦ 3 3 | 3 9 3 | 9 9 | 9 | 20
or o.3o.3o.3o.3o. & | 12 ♦ 5 5 | 30 | 30 | 10 --------------------+----+-------+-----+----+--- a. .. .. .. .. & | 2 | 30 * ♦ 4 | 6 | 4 oo3oo3oo3oo3oo&#x | 2 | * 30 ♦ 8 | 12 | 6 --------------------+----+-------+-----+----+--- ao .. .. .. ..&#x & | 3 | 1 2 | 120 | 3 | 3 --------------------+----+-------+-----+----+--- ao .. .. .. oa&#x | 4 | 2 4 | 4 | 90 | 2 --------------------+----+-------+-----+----+--- ao3oo .. oo3oa&#zx ♦ 6 | 6 9 | 18 | 9 | 20
oaoo3oooo3oooo3ooao&#xt → outer heights = 2/sqrt(10) = 0.632456
inner height = 1/sqrt(10) = 0.316228
a = sqrt(3/2) = 1.224745
(pt || pseudo a-pen || dual pseudo a-pen || pt)
o...3o...3o...3o... | 1 * * * ♦ 5 5 0 0 0 0 0 | 10 20 0 0 0 0 | 30 0 0 | 10 0
.o..3.o..3.o..3.o.. | * 5 * * ♦ 1 0 4 4 1 0 0 | 4 4 12 6 4 0 | 12 12 6 | 6 4
..o.3..o.3..o.3..o. | * * 5 * ♦ 0 1 0 4 0 4 1 | 0 4 6 12 4 4 | 6 12 12 | 4 6
...o3...o3...o3...o | * * * 1 ♦ 0 0 0 0 5 0 5 | 0 0 0 0 20 10 | 0 0 30 | 0 10
---------------------------+---------+------------------+-------------------+----------+------
oo..3oo..3oo..3oo..&#x | 1 1 0 0 | 5 * * * * * * ♦ 4 4 0 0 0 0 | 12 0 0 | 6 0
o.o.3o.o.3o.o.3o.o.&#a | 1 0 1 0 | * 5 * * * * * ♦ 0 4 0 0 0 0 | 6 0 0 | 4 0
.a.. .... .... .... | 0 2 0 0 | * * 10 * * * * ♦ 1 0 3 0 0 0 | 3 3 0 | 3 1
.oo.3.oo.3.oo.3.oo.&#x | 0 1 1 0 | * * * 20 * * * ♦ 0 1 3 3 1 0 | 3 6 3 | 3 3
.o.o3.o.o3.o.o3.o.o&#a | 0 1 0 1 | * * * * 5 * * ♦ 0 0 0 0 4 0 | 0 0 6 | 0 4
.... .... .... ..a. | 0 0 2 0 | * * * * * 10 * ♦ 0 0 0 3 0 1 | 0 3 3 | 1 3
..oo3..oo3..oo3..oo&#x | 0 0 1 1 | * * * * * * 5 ♦ 0 0 0 0 4 4 | 0 0 12 | 0 6
---------------------------+---------+------------------+-------------------+----------+------
oa.. .... .... ....&#x | 1 2 0 0 | 2 0 1 0 0 0 0 | 10 * * * * * | 3 0 0 | 3 0
ooo.3ooo.3ooo.3ooo.&#(xxa) | 1 1 1 0 | 1 1 0 1 0 0 0 | * 20 * * * * | 3 0 0 | 3 0
.ao. .... .... ....&#x | 0 2 1 0 | 0 0 1 2 0 0 0 | * * 30 * * * | 1 2 0 | 2 1
.... .... .... .oa.&#x | 0 1 2 0 | 0 0 0 2 0 1 0 | * * * 30 * * | 0 2 1 | 1 2
.ooo3.ooo3.ooo3.ooo&#(xxa) | 0 1 1 1 | 0 0 0 1 1 0 1 | * * * * 20 * | 0 0 3 | 0 3
.... .... .... ..ao&#x | 0 0 2 1 | 0 0 0 0 0 1 2 | * * * * * 10 | 0 0 3 | 0 3
---------------------------+---------+------------------+-------------------+----------+------
oao. .... .... ....&#(ax) | 1 2 1 0 | 2 1 1 2 0 0 0 | 1 2 1 0 0 0 | 30 * * | 2 0
.ao. .... .... .oa.&#x | 0 2 2 0 | 0 0 1 4 0 1 0 | 0 0 2 2 0 0 | * 30 * | 1 1
.... .... .... .oao&#(ax) | 0 1 2 1 | 0 0 0 2 1 1 2 | 0 0 0 1 2 1 | * * 30 | 0 2
---------------------------+---------+------------------+-------------------+----------+------
oao.3ooo. .... ooa.&#xt ♦ 1 3 2 0 | 3 2 3 6 0 1 0 | 3 6 6 3 0 0 | 6 3 0 | 10 *
.aoo .... .ooo3.oao&#xt ♦ 0 2 3 1 | 0 0 1 6 2 3 3 | 0 0 3 6 6 3 | 0 3 6 | * 10
aooa oaoo3oooo3ooao&#xt → outer heights = 1/4
inner height = 1/2
a = sqrt(3/2) = 1.224745
o... o...3o...3o... & | 4 * ♦ 1 4 4 1 0 0 | 4 6 12 8 0 | 6 12 12 0 | 4 6
.o.. .o..3.o..3.o.. & | * 8 ♦ 0 2 2 0 3 3 | 1 6 12 2 9 | 3 18 6 3 | 4 6
-----------------------------+-----+-----------------+---------------+------------+-----
a... .... .... .... & | 2 0 | 2 * * * * * ♦ 4 0 0 0 0 | 6 0 0 0 | 4 0
oo.. oo..3oo..3oo..&#x & | 1 1 | * 16 * * * * ♦ 1 3 3 1 0 | 3 6 3 0 | 3 3
o.o. o.o.3o.o.3o.o.&#a & | 1 1 | * * 16 * * * ♦ 0 0 3 1 0 | 0 3 3 0 | 1 3
o..o o..o3o..o3o..o&#x | 2 0 | * * * 2 * * ♦ 0 0 0 8 0 | 0 0 12 0 | 0 6
.... .a.. .... .... & | 0 2 | * * * * 12 * ♦ 0 2 0 0 2 | 1 4 0 1 | 2 2
.oo. .oo.3.oo.3.oo.&#x | 0 2 | * * * * * 12 ♦ 0 0 4 0 4 | 0 8 2 2 | 2 4
-----------------------------+-----+-----------------+---------------+------------+-----
ao.. .... .... ....&#x & | 2 1 | 1 2 0 0 0 0 | 8 * * * * | 3 0 0 0 | 3 0
.... oa.. .... ....&#x & | 1 2 | 0 2 0 0 1 0 | * 24 * * * | 1 2 0 0 | 2 1
ooo. ooo.3ooo.3ooo.&#(axx) & | 1 2 | 0 1 1 0 0 1 | * * 48 * * | 0 2 1 0 | 1 2
oo.o oo.o3oo.o3oo.o&#(axx) & | 2 1 | 0 1 1 1 0 0 | * * * 16 * | 0 0 3 0 | 0 3
.... .ao. .... ....&#x & | 0 3 | 0 0 0 0 1 2 | * * * * 24 | 0 2 0 1 | 1 2
-----------------------------+-----+-----------------+---------------+------------+-----
ao.. oa.. .... ....&#x & | 2 2 | 1 4 0 0 1 0 | 2 2 0 0 0 | 12 * * * | 2 0
.... oao. .... ....&#(ax) & | 1 3 | 0 2 1 0 1 2 | 0 1 2 0 1 | * 48 * * | 1 1
oooo oooo3oooo3oooo&#(ax) | 2 2 | 0 2 2 1 0 1 | 0 0 2 2 0 | * * 24 * | 0 2
.... .ao. .... .oa.&#x | 0 4 | 0 0 0 0 2 4 | 0 0 0 0 4 | * * * 6 | 0 2
-----------------------------+-----+-----------------+---------------+------------+-----
aoo. oao.3ooo. ....&#xt & ♦ 2 4 | 1 6 2 0 3 3 | 3 6 6 0 3 | 3 6 0 0 | 8 *
.... oaoo .... ooao&#(ax) ♦ 2 4 | 0 4 4 1 2 4 | 0 2 8 4 4 | 0 4 4 1 | * 12
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