名奇恆之府 literally means "Mansion/Organ of Constant Strange Reputation" and can be translated as "House of Eternity", "the Curious Organs", or the "Ancestral Fu" and are introduced in the Su Wen ch. 11, Further Discourse on the Five Depots, which says they are "born of the Earth's Qi, hidden in the Yin and their appearance is of Earth. They store but do not drain."
These organs all have a close connection with the Heart and Kidneys, the Shaoyin Axis and, like the Extraordinary Vessels, which are also "Curious" 奇 ("Qi") and have strong associations with spiritual cultivation practices like Neidan and Qigong. They consist of:
Formed out of Kidney Essence (精, Jing), which subsequently generates the Bones, Blood and Brain, the Marrow is the basis of most of the other Curious Organs. It is often "cleansed" for Neidan practice in exercises known as "Marrow Washing" 洗髓 Xi Sui.
It is mainly influenced through the Hui-meeting point of Marrow GB-39: 懸鐘 Xuanzhong and Kidney points, but since the Marrow is the source of the Bones, fills the Brain and generates Blood, it can be combined with the points that affect these Organs too, depending on what aspect one wishes to affect. An alternative name for Kid-14 髓府 Suifu meaning "Marrow Palace" (Huangfu Mi, 3rd Century) suggests that this point has a particular influence over the Marrow too.
The Bones are governed by the Kidneys and formed from the Marrow, but are also the containers and protectors of Marrow. In Neidan practice they are the Foundation of posture that must be erected before the Work can begin.
The Bones also represent the evolution of the universe from the Dao to the Myriad Things and the influence of Heaven on Earth. Some of this derived from Jeffrey Yuen teachings heard in discussion by his students, with the remainder on my own interpretation and meditation on this idea:
It is said in the Dao De Jing that: "The Dao produced One; One produced Two; Two produced Three; Three produced the Myriad Things."
Each limb extends from the trunk with a single bone in the upper part of the limb (the humerus and femur), which then becomes two in the lower part of the limb (radius and ulnar, or tibia and fibula). Combined, this makes three.
These then spread into the five metacarpals and metatarsals, as representatives of the Five Phases that govern the Myriad Things.
In the wrist, the eight carpal bones, arranged in two rows of four, represent the two (Yin and Yang) becoming the four cardinal, then ordinal directions, to form the Early Heaven Bagua (八卦). This is then projected onto the palm in the Later Heaven Bagua sequence which is used in palmistry.

The seven bones of the ankle, share a connection to the Seven Stars of the Big Dipper (七星 Qixiang), along with the seven cervical vertebrae and seven sensory orifices of the head. The Seven Stars of the Big Dipper have special sacred significance in Daoism, revolving around the Pole Star and are paced by Daoist adepts in ritual to connect them with these sacred stars. The Qiao Mai Extraordinary Vessels also run a course from the ankles to the head and eyes suggesting that these Vessels are connected to the cosmology of the Big Dipper. They also form an anatomical representation of the character for Dao 道 which is a head over a foot implying a "path" or "way" of life rather than a physical pathway.
The five metacarpals/metatarsals then represent the manifestation of the Myriad Things governed by the Five Phases. These are formed from Bagua map of the palm above:

As well as being influenced by the Marrow points above, as the Bones originate from Jing and Marrow, they can also be influenced by:
The Hui-meeting point of Bones
and points with 骨 Gu ("Bone") in their name, such as:
LI-16: 巨骨 Jugu
SI-4: 腕骨 Wangu
Bl-64: 京骨 Jinggu
Bl-65: 束骨 Shugu
Kid-11: 橫骨 Henggu
GB-12: 完骨 Wangu
Ren-2: 曲骨 Qugu
and points with 髎 Liao ("Crevice") in their name, such as:
LI-12: 肘髎 Zhouliao
LI-19: 口禾髎 Kouheliao
St-3: 巨髎 Juliao
SI-18: 顴髎 Quanliao
Bl-31: 上髎 Shangliao
Bl-32: 次髎 Ciliao
Bl-33: 中髎 Zhongliao
Bl-34: 下髎 Xialiao
SJ-14: 肩髎 Jianliao
SJ-15: 天髎 Tianliao
SJ-22: 耳和髎 Erheliao
GB-1: 瞳子髎 Tongziliao
GB-29: 居髎 Juliao
Du-25: 素髎 Suliao.
As also mentioned above, the Qiao Mai Extraordinary Vessels have a close relationship to the Bones and Brain and can be used to access issues relating to the Bones, Brain and Marrow.
Described as the "Sea of Marrow", this is where sense perception and consciousness (Jingshen 精神 in Chinese) are formed from the mingling of Jing 精 and Shen 神 in the upper cavity of the skull. The spinal cord is also considered an extension of the Brain where consciousness flows into the body.
In Neidan practice, the Brain is the Fire (☲ 離 Li) of the mind, which must be lowered under the Water (☵ 坎 Kan) of the Uterus in order to extract True Yin (☷ 坤 Kun) and True Yang (☰ 乾 Qian) and form the Immortal Foetus in the Uterus.
It is mainly accessed through the Sea of Marrow points:
Du-20: 百會 Baihui
Du-16: 風府 Fengfu
Points with 腦 Nao "Brain" in the name:
GB-19: 腦空 Naokong Du-17: 腦戶 Naohu
Those with strong effects on the senses and consciousness such as:
GB-20: 風池 Fengchi
Du-26: 人中 Renzhong
As well as all the scalp points of the Qi Streets of the Head, the Du and Qiao Mai Extraordinary Vessels.
The reproductive functions of the Uterus are governed by the Kidney Jing while its nourishment comes from the Blood making it a place in the lower cavity where the Shaoyin combine. The Extraordinary Vessels of the Ren and Chong also connect here and its ability to retain or discharge is governed by the Dai Mai, giving this Organ spiritual connections, especially in early Chinese religion that was mainly centred around ancestral worship, when this is the Organ that enables the ancestral line to continue.
Although the original text specifies the Uterus with the phrase "woman's seed womb", some have suggested that in men the spermatic system should constitute an equivalent Curious Organ too, or that the Uterus is still energetically present in that space in men. This is especially prevalent in the focus on the Lower Cavity to form the Elixir and generate the Immortal Foetus in later Neidan practices. Instead the character for "Woman" 女 is read as referring to the feminine, Yin, generative principle that is universal in all people. This then makes Uterus into the Water (☵ 坎 Kan), under which the Fire (☲ 離 Li) of the mind, centred in the Brain, must be placed in order to extract True Yin (☷ 坤 Kun) and True Yang (☰ 乾 Qian).
It is mainly accessed through the Extraordinary Vessels of the Ren, Chong and Dai Mai but some specific points relating to the menstrual cycle can be determined from the alchemical text Zhouyi Cantong Qi (周易參同契 attributed to Wei Boyang, 2nd century CE) . Here, the lunar cycle is represented by a sequence of 6 groups of 5 days governed by the waxing and waning trigrams. These correspond to a rotating cycle of the Early Heaven sequence, with Kan in the west and Li in the east governing the whole Yin and Yang parts of the cycle respectively.
These attributions can be mapped onto the body with the inner trigram representing the Early Heaven trigram that rules the period of 5 days and the outer trigram being its Late Heaven pair, corresponding to the Channel that governs that period. This results in a sequence that has relevance to the menstrual cycle which also corresponds to the moon.
One notable pattern that emerges is that the points which govern the 5 day periods corresponding to the ordinal directions only involve the Spleen and Pericardium, which are the channels that were chosen to open the Chong Mai and Yin Wei Mai. The cardinal directions of north and south are governed by the Heart and Kidneys that make up the Shaoyin Axis.
Another pattern is that the Yin part of the cycle draws upon the Ren, Du and Kidneys that connect to the Jing, while the Yang half of the cycle comprises of points that affect the Shen. This connects them to the principle of the Curious Organs.
The two directions that are not part of the waxing and waning trigrams are Kan and Li. These govern the 15 day Yin and Yang halves of the cycle as a whole and correspond to:
Governed by the Heart, the Ling Shu ch. 8 says "the Vessels (脈 Mai) house the Spirit (神 Shen)" and so the Vessels provide the means for the Shen to be infused throughout the body, connecting with the Jing in places like the Brain. Diseases that affect the Vessels produce "Strange Diseases 奇病" using the same character 奇 as used in the Extraordinary Vessels and Curious Organs, connecting the Vessels to these states of disorder. In Neidan practices the Heart, and hence the vessels must be quietened in order to focus on the generation of the Elixir.
They can be accessed through:
The Hui-meeting point of the Vessels
Lu-9: 太淵 Taiyuan
Sea of Blood points:
Bl-11: 大杼 Dazhu
St-37: 上巨虛 Shangjuxu
St-39: 下巨虛 Xiajuxu
Heart, Pericardium, Spleen and Liver points with a strong influence on the Blood or the Vessels, especially those with 血 Xue ("Blood"), 脈 Mai ("Vessel") or 沖 Chong ("Surging") in the name such as:
Sp-10: 血海 Xuehai
Sp-12: 沖門 Chongmen
St-30: 氣沖 Qichong
St-42: 沖陽 Chongyang
He-9: 少沖 Shaochong
Bl-3: 眉衝 Meichong
Bl-62: 申脈 Shenmai
Pc-9: 中衝 Zhongchong
SJ-1: 關衝 Guanchong
SJ-18: 契脈 Qimai
GB-9: 天沖 Tianchong
GB-26: 帶脈 Daimai
Liv-3: 太沖 Taichong
Liv-12: 急脈 Jimai
The Luo and the Extraordinary Vessels which are also 脈 Mai, especially the Wei Mai and Chong Mai.
The Gall Bladder is said to store Jing and also has a complementary relationship to the Heart in terms of the Earthly Branches, being opposites on the Chinese clock and therefore having complementary I Ching Hexagrams. It is also a Shaoyang Organ and so shares the Shaoyin property of being a Pivot. This Yang Pivot and the Gall Bladder's the ability to make judgements, enables consciousness to extend outwards to connect with the regular meridian system so it can act upon the world.
Having its own channel, it can be accessed easily through its own points and many of its points also connect to the other Curious Organs. These include:
The Brain
Du-20: 百會 Baihui
GB-19: 腦空 Naokong
GB-20: 風池 Fengchi)
The Marrow
The Bones
Bl-11: 大杼 Dazhu
GB-1: 瞳子髎 Tongziliao
GB-12: 完骨 Wangu
GB-29: 居髎 Juliao
Bl-32: 次髎 Ciliao
The Vessels
GB-9: 天沖 Tianchong
GB-37: 光明 Guangming
And the Uterus, via the Dai Mai
GB-26: 帶脈 Daimai
GB-27: 五樞 Wushu
GB-28: 維道 Weidao
Liv-13: 章門 Zhangmen
This makes the Gall Bladder a central Pivot connecting the Curious Organs to each other, as well as the Meridian system as a whole.